Wow, you really are a sh*t disturber, aren't you?
Anyhow, we could go on for hours but in a nutshell, you have the compressor wheel size which is stated as 50 trim, 60 trim etc and then you have housing sizes, IE T3, T4 etc. Those 2 combined determine how much air it can flow, in lbs/hr using charts the manufacter has for us.
Stage I/II/III etc is the turbine wheel size, Stage I is a stock turbo, stage II a popular upgrade and stage III is next inline, as you go up in stage, the wheel gets heavier and also spool time can increase based on the housing you select which brings us to-
.48/.63 and higher housings, can't remember but its a measurement using cross sectional area and the smaller housing has more direct flow, think small straw so this will help the turbo spool up faster BUT it will affect top end power, .63 is more of a bigger pipe, spool up is usually a bit later but the top end hit is worth it.
The stock garrett turbo is a T3 turbo, on both sides, a T3/T4 is a T3 center section and a T4 compressor housing, which is larger so you can make more power, more efficiently as less boost than a similar sized T3 turbo.
There is more and maybe I made a mistake but we'll start it there.