There are no S4 cars made from the A4 model during the years 1996 - 1999. The picture you show is a stock A4 model.
If you are referring to the S-Line as an S4, then no your car is not.
Audi did offer a Sport Package as an option for the A4 which included uprated sway bars and springs, 16" 7 spoke wheels and for those cars with Tiptronic, a 3-spoke steering wheel with an "S" badge on it and shift controls on the wheel. Motor was not modified.
I have seen on the web some other Audi models that were listed as sport with a higher HP engine, but not the wheels from the sport package option. I do not have any documentation for those models. It was something like 180 HP.
Unfortunately, your car is not an S-Line, as you have the sport model car, you will get these few extras, e.g the 16" Competition alloys and the Leather 3 spoke steering wheel with the 'S' badge on it.
I have the later version of your car, with the 3 spoke steering wheel with the badge on also, with the more sportier seats etc....
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