MS had their own version, just as they had Word to take on MacWrite.
Apple "sold off" MacProject when Claris came about. They got all of the programs with the prefix of "Mac" (except MacDraft, which was never an Apple/Claris program) and updated them...MacPaint 2.0 was first followed by the "II" series of programs--MacWrite II, MacDraw II, MacProject II, and FileMaker II (though that was simply a renamed version of the existing FileMaker, which I believe was purchased from a company called Nashoba).