I've said this a ton of times on here but one more time...
TFSI and TSI don't mean anything in particular, except that it's turbocharged and direct injected. In the literal sense,
both of them just mean it's a
Turbocharged,
Fuel
Stratified
Injection engine. For some reason they dropped the "FS" and just made it "S".
Doesn't mean anything about
what engine it is. It could be a 4cyl EA113, EA888, or it could be a V6 EA839 or V8 EA825, etc. These are all turbocharged, direct injected engines.
The
name "TFSI" or "FSI" or "TSI" actually being an "identifier" of the engine is borne from "VW land"/Veedub enthusiasts that saw the letters printed on their engine covers--for EA113 2.0Ts (like in "Mk5" cars)
VW printed "FSI"; for later EA888 2.0Ts (like in Mk6 and beyond) VW chose the letters "TSI" instead.
Meanwhile, for
Audis (and the 2.0Ts are all Audi-designed engine, not VW, keep in mind), Audi used "TFSI" for nearly all of them and basically interchanged the terms "FSI", "TSI", "TFSI" however they felt like. And again since it's their engine they can call it whatever they like and it will still be correct, so these letters don't mean anything since they used them interchangeably.
So you will see Audi applications having "Turbo FSI" or "TFSI" printed on [cosmetic] engine covers for both EA113 and EA888 2.0Ts, high output, standard output, whatever, all the same thing
Absolutely the easiset way to tell what family 2.0T you have is the oil filter location. You can use the engine code too but it's even easier to just lift the hood and look--is there an oil filter up top or not? The EA888s the oil filter is up top and to the left when looking in the engine bay. EA113s have the oil filter at the bottom.
Yours has the oil filter up top so there you go--it's an EA888.
Now
whether it's a Gen 1 or 2 EA888 requires a bit more looking--look to the rear of the valve cover after removing the engine cover and looking behind the coils/coil harness, towards the firewall. If you have solenoids back there, it's a Gen 2. If you don't it's a Gen 1.
The info you posted is conflicting--in one screenshot it says it's a CESA engine (this is a Gen 2), but then it says it's "208hp" which was mostly the rating for the Gen 1 engine. The Gen 2 is more commonly seen as "211hp" or "220hp", so the best way to tell here is finding the engine code on your PR sheet;
or just looking for those solenoids at the back.