Aid climbers will typically have the second (tag) rope clipped to their harness. If they need gear that is down at the belay, then they'll yell down to the belayer to tie it to the rope and the leader pulls it up (tagging gear). This only works if the leader is less than a half ropelength from the belay, unless they have a haul line as well.
Shortfixing is used when the leader can solo. The leader leads up to the next belay, pulls up all the slack rope, and ties the middle of the rope into the anchor (fixing the rope). He may also do this with the tag or haul line as well. Then the leader continues leading to the next pitch while the follower jugs the rope and cleans the pitch. Once the follower reaches the belay, he can tag up gear.