Performance halter (in AQHA/APHA/ApHA) is based on the horse's conformation.
Here is a Halter-Halter horse:
Here is a Performance Halter Horse-
Big difference right?
Halter-Halter horses (the 1st image) can't really move as well as performance halter horses.
Performance halter horses are judged on conformation, BUT they can still move normally and be ridden in classes, unlike Halter-Halter horses. Performance Halter horses are breed for different disciplines, whine halter-halter horses are JUST bred for halter.
As for showmanship, you do quadrants. Halter you do not.
--Changed some of the images for a better look at the difference--
I think in halter you only move as to not block the judges way. So if the judge is on the right side of the horse, stay on the left. Halter isn't focused on you. But that's not to say you could win first place and wear something utterly ridiculous. Halter is all about the horse, so you don't want to wear something extremely flashy. Showmanship is all about 'selling' it and making it look good.