The HDs are a Heavy Duty monotube design.
The Touring are a lower cost twin tube design.

The HDs are considered to be heavier duty and the monotube design is less prone to foaming in intense activities (like off-roading for trucks). Here is what the Bilstein web page states regarding these choices. (There is also another choice called "Sport" available for some cars):

Comfort (C) and Touring (TC) - original equipment shocks that came with your vehicle - will provide the same ride that the vehicle had when it was new.

Heavy Duty (HD) - MOST POPULAR CHOICE, Designed to work with your factory springs these will provide a firmer, more controlled ride in cars and a more stable ride in Trucks and SUV's.

Sport - Designed for use with an aftermarket lowering spring (H&R, Eibach, etc.) The Sport will be firm and actually made to work with a lowered aftermarket suspension (springs).