I found CBL Native API documentation in two places:
They look the same, but they are not. The topics in the first include subtopics of Manager, whereas the those of the second don’t. If you click the Manager page for both of them you get very different material.
Which should I use?
Both. The first link is to the overview & conceptual documentation, and the second is to the API docs that list and describe every method and property. They have different purposes. (For comparison, Apple also has both Guides and References.)
You can also use the API docs for the Cocoa implementation, which are in the comments in the header files. Option-clicking a symbol in Xcode will pop these up, just as with system frameworks. These include some things that aren’t part of the cross-platform API.