The flat tappet (WR) operates like many automotive solid tappets: it always follows the highest point on the cam lobe, whether directly above it or not. The tappet must be wide enough to act on any part of the lobe (or it will be destroyed), but the tappet length does not affect the cam duration.
The H-D roller tappet operates similarly to an automotive roller tappet: it follows the closest point on the cam lobe (tangency) beginning with the approaching side of the lobe. However, the motion is not symmetrical w/r/t opening and closing rates (even with symmetrical lobes) due to the tappet offset: the roller is always closer to the opening ramp. This is why the center-to-center distance of the 4-cam (45, K, XL, UL) intake and exhaust tappets is different than the c-c distance between the intake and exhaust cam lobes. H-D roller tappets 1929-83 are .855" OD.
There is another (non-H-D) variant: a solid (not rolling) tappet with a radiused contact surface such as Triumph "B" series. The tappet motion matches the roller (except for the friction element). Triumph tappets were produced in 3/4", 1-1/8" and 3" radius (among others).
In both of these cases, the tappet radius (or roller radius) greatly affects the events: a larger diameter radius makes contact earlier and acts differently during both opening and closing events. Obviously, a flat tappet has infinite radius.