Yes, I think that's basically correct, although there are different kinds of intuitionism and constructivism, so I suppose the answer will depend upon to whom you are speaking. For example, you have the option to study constructive objects with classical logic, classical objects with intuitionistic logic, and other combinations. There is also the freedom in which axioms you have in your bedrock intuitionistic logic.

I'm not particularly clear on all of these distinctions myself. I wrote another article on Plus about this sort of thing, and my distinguished intuitionistic colleague Douglas Bridges thought it was OK so you might want to take a look. But he also said that some points were not properly developed so take it only as a starting point!