TFSI is the engine type which is used by VW/AUDI in almost all their cars and stands for Turbo fuel stratified injection.
Quattro (means 4) is the all wheel drive technology of Audi. By non Quattro means it's a FWD car. A3 Quattro is available on 2L displacement and it's standard feature here in US. On 1.8 it's FWD only. That's the reason of a better mileage too Quattro system gives slightly less MPG.
For Mercedes it's 4matic. BMW has Xdrive.
Quattro drive system in below picture . You can see a shaft to rear wheels. Though its an AWD but Power is send to rear when required.