The non-static inline function declaration refers to the same function in every translation unit (source file) that uses it.
The One Definition Rule requires that the body of the function definition is identical in every TU that contains it, with a longish definition of “identical”. This is usually satisfied provided that the source files all use the same header, and provided that the function doesn’t use any global names with internal linkage (including static functions) or any macros that are defined differently in different TUs.
I don’t remember encountering that particular linker error before, but it’s at least possible that one of these restrictions is responsible. It’s your responsibility to satisfy the requirements: undefined behavior with no diagnostic required if you don’t.
The static inline function declaration refers to a different function in each translation unit, that just so happens to have the same name. It can use static global names or macros that are different in different TUs, in which case the function might behave differently in the different TUs, even though its definition in the header file “looks the same”.
Because of this difference, if the function contains any static local variables then it behaves differently according to whether it is static or not. If it is static then each TU has its own version of the function and hence its own copy of the static local variables. If it’s inline only, then there is only one copy of the static local variables used by all TUs.