A7750 means Asian 7750. Valjoux 7750 is actually the gen movement...or ETA 7750...same thing really. "Asia Valjoux" means Chinese copy of the Valjoux 7750. There was an earlier slow beat movement that was still an A7750...but the smooth sweep 28.8k movement is the usual one. You can still get collectors selling the slow beat movement which some people want as the hand sizes used on the slow beat are the same for the Swiss Valjoux...so if you're planning on putting in a real Swiss engine...getting the rep with the slow beat movement makes life easier.
I have no idea what 7750b1 is.
Auto means mechanical movement...NOT quartz. This means it requires kinetic movement to wind the watch via the rotor. Less reliable and more finicky and more costly to maintain than quartz...but closer to the gen...and nifty to have a fully mechanical thing beating on your wrist.
Reps look great. They feel great (for the most part). With a real Swiss movement are essentially as reliable as a gen (but approaching the $1000 mark for a Valjoux 7750 chrono rep...but around $300 for an ETA based non-chrono). A $300 rep, serviced properly, can give you a lifetime a service...the same as the real deal, with the same reliability, durability, accuracy as the gen...but usually hit and miss on the water resistance. The problem is finding someone who can service the reps.
Read The Zigmeister's movement reviews for an idea of how good these movements are as some suck, and some don't. I think you can link to them from my Noob Guide...can't remember.