For a software, I have two different branches, that only differ in using different library versions of a package, that my software uses. The API of this library has changed between the versions in a non-compatible way.

I am currently developping using both versions with the identical functionality in different branches, the only difference exists during building and loading of shared libraries.

Should I release these packages with different version names using Semantic Versioning? In my opinion, yes, but what about the naming of these different versions?

Currently I am using the "normal" numbering using the new version of the third-party library, e.g. 1.0.0, and a suffix for the version using the older third-party library, e.g. 1.0.0-json-c-0.10, see https://github.com/residuum/PuRestJson/releases