meaning - "Some characteristic C is what distinguishes A from B"

It depends on what the subject matter is. As the subject matter changes, (C) changes in distinguishing (A) or (B).
In your case, the fact that "imposing restrictions on the available resources"(C) is an action distinguishes it from being part of "computability theory"(B), so "imposing restrictions on the available resources" belongs to "computational complexity"(A)