Generally speaking, once a file is open, its path is no longer relevant. In some poorly-written programs (like TextEdit, last I checked!), if you open a file, move it, and then save changes, it will create a NEW file in the location the original was opened from. But most apps will even save it in the new location the way you would (or should) expect.
The Mac OS has always been pretty smart about this. Actually, the classic Mac OS was smarter than OS X, since OS X has some Unix baggage that's not so smart.
The technical reason is that once a file is open, it's accessed from a pointer which never changes. For saving it's a little more complicated, because the program needs to know the path to save it to. The Classic Mac OS, and more savvy OS X apps, use a many-layered process to identify files. It only uses absolute paths as a last resort. This is also why you can make an alias to a file, move the original and have the alias still work. On Unix you can't do this. (I don't know about Windows off the top of my head.)