"X-Anusati" basically means "go over the memory of X" ("anu" is literally "under" but it has connotation of following something, in this case following a memory).
"X-Bhavana" means something like "generate X", "cultivate X", "produce X".
As you said, both involve the act of Calling something into mind (what you call "active thought") and then Mulling Over it (what you called "sustained thought").
The Mulling Over part is the same in both cases but the Calling part differs. In case of Anusati the emphasis is on recalling something we know from before, while in case of Bhavana the emphasis is on creating or manufacturing something new.
In practice, however, there is not that much difference, since in case of e.g. buddhanusati we have not actually experienced Buddha first-hand and have to manufacture his image from conceptual elements we know of. Conversely, in case of asubha bhavana it's not like we create the disgusting images completely from scratch, we assemble them from memories of disgusting things we have experienced before.
Why they are named differently? I guess, that's because in case of X-anusati that "X" refers to the source memory - while in case of "X-bhavana" that "X" refers to the target state.
Indeed, it would not make sense to call it "metta-anusati" or "asubha-anusati" - because we are not actually remembering metta or asubha, we're generating them. Similarly, it would not make sense to call it "buddha-bhavana" or "sila-bhavana" - because we are not cultivating Buddha or our sila, we are remembering them.