This has been a contentious issue in the history of philosophy. Wittgenstein and the Logical Positivists claimed that metaphysical arguments are just linguistic. That can't be true, of course--not in the usual sense of "linguistic" because you can translate the arguments from one language to another. A theory of truth could first be formulated in Polish and then translated to English, and the arguments against it that were first formulated in Polish could then be translated into English as well. If the argument were just an argument about how to use a language, how would that be possible?
However, there is a related position that focuses on concepts rather than on language. Concepts are language-independent. The same concept can be expressed in multiple languages. It makes sense to say, for example, that there are two different concepts of truth, regardless of which language you express those concepts in.
The question then comes down to whether there is one concept that is right and the others are wrong. I like to use the analogy of sets and relations. A set is the normal mathematical construct that everyone knows. A relation is a bit more obscure, but it is easy to describe: basically, a 2-ary relation R is an extensional association between two domains X and Y. If x represents a member of X and y represents a member of Y, then R(x,y) is a proposition that is possibly true of some x and y, and possibly false of others. A 3-ary relation has three domains R(x,y,z), and in general an n-ary relation has n domains.
Now we get to the example. It is common in set theory to say that a relation is nothing but a set of tuples. That is, if R(x,y) is true, then this means the pair <x,y> is in the set R. So there are only sets; relations are reducible to sets. On the other hand, you could say that a set is just a 1-ary relation. That is, if x is an element of S, then this just means that S(x) is true. So there are only relations; sets are reducible to relations.
Which is true? Are relations just sets or are sets just relations? Both sides of the argument are making a different claim. This isn't just a case of people using words differently. It's not a mere linguistic disagreement. But it is simply not the case that one of the positions is in any absolute sense correct and the other position is incorrect. They are both correct.
Does the same apply to all metaphysics? It's plausible that it does apply to a lot of metaphysics, but there are cases where it seems not to. One example where it doesn't seem to apply is your example of definitions of truth. This is because making a claim relies on your notion of truth. If we are to take the coherence camp at their word, then all they are saying is
(1) It is coherent to believe that truth is what it is coherent to believe.
This is much different from what the correspondence theory of truth implies. In the correspondence theory of truth, the coherence theory of truth is
(2) The fact of the matter is that truth is what it is coherent to believe.
By contrast, when the coherentist expresses the correspondence theory of truth, he is saying
(3) It is coherent to believe that the truth is what corresponds to the facts.
but what the correspondence advocate is saying is
(4) The fact of the matter is that truth is what corresponds to the facts.
For myself, I don't find (1) or (3) to be very interesting claims. So it's coherent? So what? I want to know whether (2) and (4) are true, not (1) and (3). So at least in this case, there seems to be a difference that goes beyond conceptualization.