So will clang, gcc, and msvc all have different implementations modules?
But modules themselves are standardized, and so you should expect that after some time, you'll have stuff that works on all implementations. I don't believe that any of them are complete yet, which is why you see these differences currently.
(Caveats: I have followed the development of modules semi closely but am by no means an expert.)
But modules are very new and I doubt if enough corner cases are nailed down yet.
For generated code, definitely. But for example their standard libraries are different so you still can't, say, compile something in gcc that uses std::string and expect to be able to link it to something compiled with clang that uses std::string unless you are careful to use the headers (and .a files) of the same libc++ or libstdc++
I consider this a feature, not a bug -- diversity in implementation is a plus.