UCI and BIU are two different governing bodies/styles of trials riding. UCI is the same UCI that runs world cup XC, DH, etc. BIU is a trials-specific series.
BIU rules allow the use of pedals and bashring (or bashguard on mods) without counting dabs. UCI rules don't allow pedals, so if you set your pedal or bash on something, you get a point counted. This difference has made all types of bike setup changes between the two (UCI bikes have gotten teeny bashrings and people running 16t front rings for more clearance, up to 8cm (!) bottom bracket rise to give higher clearance, other randoms I can't remember)
More people are converting to UCI rules, which IMO is cleaner, using only tires, but to each his own.....
A lot of UCI riders use pinned platforms, for their better grip, and a lot of BIU riders use cages for their durability when doing pedal hooks (I've personally seen a guy pull off a shoulder-height sidehop to a ledge by hooking his pedal.)