For me the most defining difference are usually the so called Hidden Object screens in HOGs, which aren't about picking up useful items you need for your adventure but about finding a bunch of
random items that have hardly any connection to it, according to some list of words, just for the "fun" of it, as some kind of detached puzzle. It often ends with you getting an item you need, but the way how you get to it doesn't really make sense in terms of story-telling.
Games like Tiny Bang Story, Samorost, possibly My Brother Rabbit share similarities with HOGs (simple gameplay that often just comes down to clicking the right spots on screen*) but don't have this common element of the other games in the genre, so they're somewhere in between. Then again, Samorost has an actually character who's going places and doing things and who's visible on (almost?) every screen, which is different from Tiny Bang Story where you're just an incorporeal onlooker who's traveling from screen to screen, so to me Samorost is still closer to point-and-click games like Machinarium, even if you don't directly control the character. This doesn't really work as defining criterion though, as most HOGs have characters following a story, too, though usually in first person perspective.
To me HOGs seem inspired by FP puzzle/adventure games like Island of Dr. Brain and Myst, but mixed with Where's Waldo, more casual puzzles, more sparkle and constant reward mechanisms.
(* Of course you can say that about P&C adventures, too, but there it's often a more complicated combination of clicks.)