Since it doesn't look like anyone gave a full answer to this, I'll chime in.
The two types of tappets (also called cam followers or lifters) in common use today that I'm aware of are flat and roller. The tappet rides on the cam and follows the lobe to transfer the lift to open and close a valve. The name describes the part of the tappet that physically rides on the cam - either a flat metal surface or a roller. As you can imagine, the friction of flat metal against the cam if much higher than a roller riding over. That is why people are talking about the need for zinc and/or other additives necessary to prevent cam wear on a flat tappet type of system. I'm not going to comment on whether it's needed or not, that has been beaten to death and beyond already.
Flat tappets on the left, roller tappets on the right.
