I think you are right in that the primary mechanisms remain the same, or at least similar, but that was not my point anyways. The surrounding adjectives describe more the context of which capitalism exists within.

The effects and consequences of capitalism under feudalism or the age of slavery is, for example, fundamentally different from capitalism under a freer modern democracy. A slave or serf did not have the opportunities of capitalism, which changes how the system behaves and its effects.

The term "capitalism" becomes kind of meaningless, because it just describes a broad set of mechanisms. In the case of the question in this thread it is much more descriptive to include the context of which it exists within.