God, this thread is all over the shop!
The engine covers won't determine the trim level - up until this year when the 105bhp TwinAir was offered, all TwinAir 500s were the 85bhp one, regardless of what the engine cover looked like - generally 2011-2013 have painted (red & white) lettering on the cover, from 2013 onwards it's plain black.
The TwinAir engine was offered to start with on Pop, Lounge & Sport, as per the other engines. However, Fiat quickly stopped offering it on the Pop trim and then phased out the Sport trim & replaced it with TwinAir & TwinAir+ - none of them had a different version of TwinAir engine, it was
just the trim levels that were different. The easiest way to spot a TwinAir+ is it'll have 16" alloys instead of 15" ones on the TwinAir, and it'll have climate control instead of manual air con, amongst other things. They were all badged 'TwinAir' on the bootlid, but they don't say + or plus if they're a plus, so you have to look at the equipment to determine this.
You'll find a handful of TwinAir Pop & Sport models, but not many.
Fiat then dropped the TwinAir/TwinAir+ trim levels and replaced them with 'Street' - unlike TwinAir/TwinAir+ the Street was also available with the 1.2 engine and 1.3 Multijet. This only ran for a very short time and they then dropped it and brought in the 'S' trim, which we still have today, which also has all the engines available.
In summary, you can have many models with a TwinAir engine, but if the spec name of the car is 'TwinAir', it'll only have a TwinAir engine - clear as mud