audio designers usually make sfx and fx noises.
they are responsible for every single sound effect used in a game. A gunshot, a door closing, footsteps, a monster growl, animal sound, etc.
an audio designer will make these noises by either live recording actual sounds from field work. (The guys at DICE on Battlefield Bad Company recorded real tracks of each and every gun in the game. They also researched echo and reverb based on the environment, and made sure to implement this into the sound) An audio designer will even synthesize his own sounds by manipulating current sound effects till they are pitched exactly as the audio guy wants.
For ex. i once saw a guy who made a chime effect by recording the sound of him hitting two hammers today, then he manipulated the original sound using software until he had created a really unique chime sound.
a music composer writes entire scores and compositions for the game.
hope that helped