Yep, the TC means "touring class" It' bilstein's base shock/strut. PS, you have struts. The difference is that a strut is a shock that also has other stuff on it and serves as the upright in the mcpherson syspension.
The TC also comes in TC sport, it's bascially the same thing but for a lowered sport suspension.
The HD is a stiffer shock. At that level I would also consier the koni yellows and koni reds, depending on what you want. Also, many people find the TCs fine for the MK3 cars, for some reason, the MK4 tc struts tend to be bouncy.