In beat em up games, characters typically have movelists that look like sequences of punch punch kick punch (like in Bayonetta) and the funny thing is, the later moves in that combo will be different than your ordinary punch. If you mash slash with Dante in DMC 3 times, he will do a different move every time you press the button. This is what beat em up games call a Chain. Rather than having access to all the moves all the time, you essentially have generic context sensitive attack buttons that aren’t bound to specific commands. Bayonetta’s punch and kick buttons don’t refer to a specific punch or a specific kick, they differ based on the context of the punches and kicks that came previously.
In a fighting game, Chain Combos are very different. In fighting games, all the moves do the same thing every time you activate them. Chain combos in fighting games refer to lists of moves that cancel into one another when you hit the opponent. Like in Marvel vs Capcom 3, typically your light attack cancels into medium, cancels into heavy, cancels into launcher. In Guilty Gear, punch cancels into kick, close slash, far slash, heavy slash, dust. Another salient feature of these is that you can actually cancel from any lower move in the chain into a higher one, so you can go directly from light attacks to heavy attacks, skipping anything inbetween. So if I pick up a new character in a game with chain combos, I can see what their moves are, and use them as the situation is appropriate.
The thing is, fighting games have other types of combos too, like jump-in combos (because landing on the ground cancels your aerial attack.), juggles, links (where a move stuns an opponent long enough that you can get off another attack before they can recover), and cancels into special moves.
I think a lot of beat em ups, except Devil May Cry, end up just having you work from a dumb combo list, it’s less trying things out and seeing how you can create a combo off the situation available to you, and more memorizing and reciting whatever is on the combo list to play out the exact combo they intended you to. And for a game like Bayonetta, that combo list seriously long. I want to see more individual hits that work together rather than moves hidden behind these combo chains, because then you get drastically different moves working together rather than only specific moves coming out at the end of a chain sequence.