Well, I have used "Normal" Lugs for Equipment Grounding purposes in Transformers, Gear and Panelboards - mostly because there will be a bunch of similar Lugs
(i.e. "Box of misc. Lugs from the shop"),
but more specifically, because of the need for multiple Landings.
I have dealt with Equipment using the Copper Lug in Electure's image above, for Line ("Power") Terminations.
Lighting Contactors, some Motor Starters, and a few Control Panels used those Lugs.
Now, on the other hand, I don't see much of a use for Line ("Power") Terminations using the Lay-In-Lug also posted in Electure's message!
That one pretty much is a "Grounding-Only" Lug!
(extremely useful on Grounding Bushings)