Firstly,
there's no such thing as an S-Line TT-S. It's one or the other, not both. The
S stands for "Sport" and is a separate model to the base car, with what is usually a number of improvements for performance. Most notably, the "S" spec engine is almost always unique to that version of the car; also additional things like larger brakes, better suspension, different body parts/aero, also apply.
S-Line is merely a trim enhancement on "regular" versions of a car, like the A or Q prefix models. So you could have an
A4 S-
Line or a TT S-Line but these are
not the same as an
S4 or a TT-
S. S-Line "packages" have varied on what they include over the years (and probably by country as well). Sometimes they complement other trim levels or packages and sometimes they themsevles are the trim level. It pretty much always includes exterior adornments--different bumper(s), mouldings, badges. Sometimes it additionally includes things like S-Line seats, suspension, door sills, badges and other minor interior/trim items.
From there we need to talk about quattro GmbH. quattro GmbH (renamed Audi Sport GmbH since 2016 or around there) is an Audi subsidiary who is responsible for designing and advising on changes for S cars as well as for manufacturing
most RS cars or at least major components on them like the engine. I say most because while they used to manufacture all RS cars, eventually Audi started building various RS models themselves as the RS brand/line got expanded to many more cars than the original few that got an RS model. Very early S cars like the S2 and perhaps the Ur-S4, etc. were also made by quattro gmbH but most S cars since are made by Audi simply with quattro gmbH input. This is one thing that always made RS cars more special than S cars--not only were they obviously higher performing but they were also much more limited in production numbers. Like BMW's M division there is a manufacturer distinction in the VIN as well...
In US/Canada at least:
A vehicle made by Audi will have a VIN starting with
WAU
A vehicle made by Audi Sport gmbH (quattro gmbH) will have a VIN starting with
WUA
At one point in time
S-Line specific parts and adornments were also designed and manufactured by quattro gmbH but like the RS cars and engines which all used to be made by quattro GmbH, eventually S-Line additional parts and features became just made by Audi. I could be wrong but I don't even think Audi Sport GmbH advises on or is consulted with for most S-Line stuff any longer, it's just "regular Audi".
Black Edition.
So this part I could be mistaken on because this was not a thing we had here for Mk2 TTs. But
my understanding of it is Black Edition was pretty much the same as what we call Competition Package over here--it adds things like the fixed wing "from the RS", as well as specific Competition/Black Ed bumpers, grille etc. Presumably with Black ed. it's all stuff in black, given the name. It's entirely an appearance package--there are no performance upgrades with it at all. Brakes are the same as on the base car, engine is the same as any other standard 2.0T, etc. Over here an S car
could be fitted with Competition Package but not until the last year or two of the Mk2. These cars are very rare--an S model with Competition on it.
The above meant it's much more likely to find a standard TT S-Line Competition over here (with all the racy looking bits) than it is to find a TT-S with it. Also meant for 2-3 years you could get a standard TT w/ S-Line & Competition where the S was simply not as racy or sporty
looking but was the better car. The S having the more potent engine, the bigger brakes; plus the magnetic ride suspension and variable exhaust/steering/throttle (the "S button").
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