No, inlining replaces it at the place of call. Every call, even if there's multiple of them in the same file. The idea is that, by putting the implementation in the .h file, you're signaling that you don't want to pay the overhead of the function call. (Same thing with the "inline" keyword.)

Now, if your function is sufficiently complicated, the compiler may choose to not inline it anyway (with the definition of "sufficient" being compiler-dependent).

It could be considered a compiler bug that a function with a static variable in the body could be inlined. As you say, that changes the behavior of the function. Or perhaps it could be considered a specification error - I don't know if the standard prohibits inlining in this circumstance, but perhaps it should.