Yup. In compiled-languages land it's common to see things that are API-compatible but not ABI-compatible: the compiled objects don't work together, but if you recompiled the same source code it would work with no changes. This happens (sometimes) when you do things like reorder members of a structure or switch to a larger integer type for the same variable.

C and libc have been ABI-stable on most platforms for decades. C++ on some platforms (e.g., GNU) is stable with occasional ABI breakages in the standard library; on others (e.g., MS Visual C++) it breaks with new compiler versions. Rust isn't ABI-stable at all and has no clear plans for it, despite a strong commitment to API stability (i.e., old code will compile on new compiler versions). Swift 5 is targeting ABI stability.

To save you the read: in web terms, the API is e.g. Stripe and the ABI is HTTP.