Anvil Studio uses (and I'm guessing here) Direct Music to play back midi files. How you hear it in AS is how it'll sound when played on every computer using Direct Music to play back midi. Game Maker, RPG Maker XP and VX, and other programs use Direct Music to play back midi.
Windows Media Player plays midi using samples from your sound card. Sound will vary when played back on WMP on other computers because soundcards come with different [quality] sound samples.
It's best not to adjust sound to your sound card (Windows Media Player) and to trust the sound coming from Anvil.
Of course, I could be wrong about everything posted above (I'm pretty sure I'm close, though)...