Trade Support vs Trading Assistant

Trade Support is mostly back/middle office work and has almost nothing to do with a trading career that most people think of. You're most likely going to be debugging operational issues (trade breaks, why orders aren't processing, basically IT related matters) and helping the traders fix any other problems they may have on their trading platform (my trading ticket said this order should have settled 2 days ago but it still hasn't! or why was this entered as a buy? I definitely entered this as as sell). You will rarely, if ever, learn about how to actually play the game of trading itself - sure you'll learn the mechanics of submitting an order, but not the strategy behind itself of why you made that order. You pick this role if you want to stay in an operations career. 

Trading Assistant is typically the entry level position to pursue a trading career, effectively an apprenticeship (Junior Trader is another commonly phrased role). While your roles will still be heavily operational and have many overlaps with Trade Support when you first start out (trade reconciliation, P&L accounting, etc), your end goal is to become a full fledged independent trader one day. You'll typically be assigned under a senior trader where you learn about the markets, idea generation, and how to manage your book. You pick this path if you want to pursue a trading career.