The simplest answer would be:

• Fixed capital = machinery and facilities, as opposed to

• Circulating capital = raw materials and labour power.

On the other hand,

• Constant capital = machinery, facilities, and raw materials, as opposed to

• Variable capital = labour power.

Each disjunction serves different purposes, but the first one plays a secondary role within Marxist theory, and is more or less consensual among Marxists and non-Marxists. The second one, on the other hand, is central to Marxist theory, but its significance would be, I suppose, disputed by non-Marxists.

Luxemburg claims that Smith confuses the distinctions, making fixed capital = constant capital, and she might be correct about that. Thence "for [Smith], fixed capital is the same as constant capital in marx; but [L]ux[emburg] claims that [Smith's] analysis makes constant capital disappear". If I correctly remember, she does make that exact claim, but I am not sure it is in the context of the confusion between fixed capital and constant capital. The argument would rather be that Smith enters into a kind of unwarranted regression, in trying to establish the principle that all value is a product of labour: instead of considering, like Marx, that constant capital is dead labour, and that its value is merely transferred into the new products, he attempts to explain that the items consisting in constant capital are themselves the product of labour, so that the value created by them is also indirectly produced by labour. In this way, he annuls the concept of constant capital; all capital is variable because all capital is ultima ratio reducible to labour. And, with even more reason, "capital" becomes an a-historical entity; the fact that fixed capital, at some point in the past, consisted in goods that were not produced within capitalist relations is lost, as is the distinction that Marx underlines in his critique of the Gotha program: value is not wealth, and wealth is not value, even though they largely intersect in a capitalist society.

That might be related to Smith's confusion of constant and fixed capital (if he misses fixed capital's specificity, which is to transfer its value to new products only gradually and along the duration of several sucessive production cycles, he might think of facilities and machineries as merely another kind of raw material in production, and this might be tied to his confusion between dead labour and live labour - in reducing all capital to labour, the specificities of each kind of capital are possibly lost). But then I am no specialist in Smith, and might be getting the finer distinctions wrong here.

The simplest answer would be:

• Fixed capital = machinery and facilities, as opposed to

• Circulating capital = raw materials and labour power.

On the other hand,

• Constant capital = machinery, facilities, and raw materials, as opposed to

• Variable capital = labour power.

Each disjunction serves different purposes, but the first one plays a secondary role within Marxist theory, and is more or less consensual among Marxists and non-Marxists. The second one, on the other hand, is central to Marxist theory, but its significance would be, I suppose, disputed by non-Marxists.

Luxemburg claims that Smith confuses the distinctions, making fixed capital = constant capital, and she might be correct about that. Thence "for [Smith], fixed capital is the same as constant capital in [M]arx; but [L]ux[emburg] claims that [Smith's] analysis makes constant capital disappear". If I correctly remember, she does make that exact claim, but I am not sure it is in the context of the confusion between fixed capital and constant capital. The argument would rather be that Smith enters into a kind of unwarranted regression, in trying to establish the principle that all value is a product of labour: instead of considering, like Marx, that constant capital is dead labour, and that its value is merely transferred into the new products, he attempts to explain that the items consisting in constant capital are themselves the product of labour, so that the value created by them is also indirectly produced by labour. In this way, he annuls the concept of constant capital; all capital is variable because all capital is ultima ratio reducible to labour. And, with even more reason, "capital" becomes an a-historical entity; the fact that fixed capital, at some point in the past, consisted in goods that were not produced within capitalist relations is lost, as is the distinction that Marx underlines in his critique of the Gotha program: value is not wealth, and wealth is not value, even though they largely intersect in a capitalist society.

That might be related to Smith's confusion of constant and fixed capital (if he misses fixed capital's specificity, which is to transfer its value to new products only gradually and along the duration of several sucessive production cycles, he might think of facilities and machineries as merely another kind of raw material in production, and this might be tied to his confusion between dead labour and live labour - in reducing all capital to labour, the specificities of each kind of capital are possibly lost). But then I am no specialist in Smith, and might be getting the finer distinctions wrong here.