It would do well to separate the question into two, one being about Marx and Smith and another concerning the differences between Marxism and bourgeois economic theory.
In point of fact, Adam Smith was a key contributor to the development of the Labor Theory of Value as was David Ricardo who followed on his heels. It was then Marx who took the LTV to its full logical development, whereupon the bourgeoisie had to throw out classical economics and start over lest that classical economics be taken to its logical (and, for the bourgeoisie, imminently dangerous) conclusion both in theory and in practice.
Marx expounded on the Labor Theory of Value to show that according to the Labor Theory of Value (which was the theory of value that was used by Thomas Hobbes, John Locke, Adam Smith, David Ricardo, etc) capitalists (owners of the means of production) exploit workers by depriving them of value that workers themselves create. According to Marx and in simplified form that neglects rent, interest, depreciation, etc., profit is the difference between the value that the worker has created and the wage that the worker receives from his employer.
Once Marx firmly established this principle, the Labor Theory of Value was criticized and abandoned by supporters of capitalism.
The closest thing to a bourgeois critique of Marx is by Eugen von Böhm-Bawerk and it dates back to over 100 years ago. While others have criticized small slivers of Marx's work, Böhm-Bawerk's is considered to be "comprehensive". It is astonishing how many footnotes on the "total debunking of Marx" end up leading exclusively to him. In fact, Böhm-Bawerk's work is structured to look exactly like an anti-matter version of Marx, i.e. a three volume Capital and Interest. The actual theory is thin stuff indeed, focusing on the term or period of capital.
I forget who said it but somehow Böhm-Bawerk stepped on Adam Smith somewhere in his writings against Marx and one of the neo-Smithians referred to him as "that bombastic flea, Böhm-Bawerk".
Do you know what else the bombastic flea "contributed"?
He is one of the "founders" of "Libertarian Economics" (the so-called Austrian School)...
Modern Libertarian political philosophy was born in exactly the same way as Eugene. It was "discovered" and funded by capitalism as a bought-and-paid-for ideological "criticism" of Marxism. The first important "Libertarian" institutions in America (in the early 1930's - imagine that! during the Great Depression... what a coincidence?) started out by popularizing the bombastic flea's work and distributing his books, free, to libraries and schools.
It is one heckuva of a story but the whole "Libertarian" racket was more crooked than a Ponzi scheme, absolutely manufactured out of whole cloth to oppose socialist ideology and nothing more. It is a designer theory that was designed to fulfill the needs of a free market. The demand was there for an oppositional theory to Marxism, but no supply. You can imagine how high the price was... although it fell right back down to its value when the Universities solved the crisis of production.
The reason that Libertarianism is reminiscent of Marxism is that it took it's technique entirely from Marxism but it was born as anti-Marxism or "Bizzaro Marxism" (I wasn't just joking about that reference). In fact it is fairly unique among political and economic ideologies in this regard, with only Creationism and a few others of this type coming to mind. Just as with Creationism's battle with Darwin, the Libertarians simply could not accept the direction of Science and set out to overturn it. The pioneer in this space, Carl Menger, was a contemporary of Marx but already saw in the political economy of Adam Smith and David Ricardo the seeds of the Marxist evolution, with Saint-Simon acting as the Nostradamus of the coming storm. Menger's student, Eugen von Böhm-Bawerk wrote the first "definitive criticism" of Marx's political economy. The resurrection of Libertarianism in the 1930s was not just in direct response Bolshevism but also to New Deal policies and Keynesianism, which were seen as surrender to "socialist principles" and it is not by accident that the doctrine was inextricably linked with Ayn Rand and Joseph McCarthy in post-war America. In all of this, Libertarianism never even found the time to "revise" the history of the "natural evolution" of Libertarian economics from classical political economy (to which it had previously been uniformly hostile), nor even to "discover" an underlying formal "philosophy" until the 1970s when Hayek's books were given free by groups like the Olin Foundation to universities in much the same way as Bawerk's had been before.
Virtually every "theorist" of the ideology began as a virulent anti-communist well before they were "theoreticians," Oddly, few of them bother to hide this. Virtually all of them admit to setting out to overturn a science, the implications of which, they simply could not accept. The principle cornerstone of that science inevitably begins with "The Labor Theory of Value."
with the attempt to depict Austrian economic theory, and marginalism in general, as fundamentally free of any political taint, Hayek declared (1973):
"I can find no indication that Jevons, Menger, or Wairas, in their efforts to rebuild economic theory, were moved by any desire to revindicate the practical conclusions that had been drawn from classical economics. Such indications as we have of their sympathies are on the side of the current movements for social reform."
Hayek here missed the point, however. The question does not concern Austrian (and marginalist) economics as a defense of laissez-faire capitalism against social reform, but as a defense of the basic market economy (private ownership of the means of production) against socialism (collective ownership of the means of production, first by the state and later collectively in a post "state capitalist" indeed post-state form when the state has "withered" as the bourgeoisie is fully vanquished and only a single class remains).
Hayek ignored the theoretical crisis that existed in economics on the eve to the marginalist revolution (at least in English-speaking countries). Friedrich von Wieser testified to this crisis in his biographical notice on Menger (Wieser 1923). Both he and Böhm-Bawerk were deeply troubled as they began their careers as economists. Among the problems confronting them were the implications of the classical theory of value. If that theory were true, then:
"Is not the socialist critique of current conditions, is not Karl Marx with his theory of surplus value, totally correct? Is not socialist theory just the completer of the classical idea, which the classical economists themselves did not have the courage to think out to the end?"
Frank A. Fetter was another scholar who saw the emergence of marginalism as a deliverance from an ideological dilemma. Fetter (1923) elaborated on the predicament of classical economics after the middle of the nineteenth century. Of Ricardo and his LTV, Fetter stated (1923; see also Ross 1991):
"...with his sophistical arguments he had given to this really primitive conception the phenomenal authority of his name, and it was to go on exerting a tremendous and evil influence in ways then all unforeseen. Labor is the source of value (exchange value, virtually market price as he used it); labor is the cause of value; labor produces all wealth. Naturally follows the ethical and political conclusion: if labor produces all wealth then labor should receive all wealth..."
The science simply could not be left to the scientists. With their search for "abstract truth," they had simply ("tragically") justified the revolutionaries...
Now, to the underlying and really salient question: What is value?
Everything that is produced by human beings is a "use value." The term is a "null term" in effect. A thing would not be produced unless it satisfied some human want or need, real or imagined. Further, its usefulness is a function of the properties of the thing produced. The appropriation of even the simplest elements of nature requires the exertion of labor and thus counts as "production," i.e. it would not occur without some "use" as its precondition.
Any product of labor that enters into exchange acquires a "value." The expression of that value is called an "exchange-value" of which one form (that of an exchange value expressed in money) is "price." The process of exchange represents an abstraction away from the physical properties of the products under consideration and thus away from use values as a whole (because use values have no existence apart from the physical properties of the products of human labor). Instead, exchange value and the value underlying it, gauge a social quality that is layered on top of (or "congealed" in) the products of human labor when they enter into exchange. This value appears to be no less a property of those products than their physical properties despite the fact that no electron microscope of any intensity has yet been invented that can find a single iota of value in a bar of gold. This is the basis of "fetishism."
This attribute of commodities is common to all commodities and thus to all products of human labor intended for exchange, whether or not that exchange is realized and thus all "intermediate" goods, industrial capital, etc., also have this character. On occasion, things that are not products of labor may also acquire exchange values but this is mainly an artifact of the surrounding production of commodities. There is also a detailed discussion of this in both Marx and the preceding classical economists.
The nature of the labor that makes up "value" is that it is labor of a "peculiar sort," according to Marx. It too is abstracted away from the specific physical labor that creates use values. Marx calls it "abstract social labor" and it is clearly a social average which reaches across the specific traits of the laborers to achieve an average duration and intensity. It is also a kind of labor which reduces the widely varied skill levels of many types of labor to a common denominator. It is not necessary to debate this as this was “documented” in the earliest forms of exchange and has not been challenged in any of the critiques of classical Political Economy. The art critic may argue that there is no commonality whatever between the talent that produces “Sofa Art” and the genius of DaVinci, but that same critic has to concede that, to the extent that both paintings are commodities, that “commonality” is established and reconciled every day (even if it is at a ratio of 1 million to one).