Mash flow is the very simple concept of what exactly your fingers are doing while you're fighting a group of enemies in a beat 'em up game. There are a handful of integral types, and while there are many subtle strains of these types, I'm going to break down and scrutinize the big boys.
Type 1: Super Traditional
I call this Super Traditional because the very first generation of beat 'em ups (specifically Taito's Renegade and Technos' Double Dragon) took a two button approach. The input scheme was identical; one button was for punch and one button was for kick. Either button would start a very straightforward combo that you could either see to the end, cancel by ceasing input, or get hit out of. It is very important to note there was no interplay between the two basic flows, it just seemed like it because you could start one combo in the middle of the other. What's fascinating to me about the manifestation of beat 'em ups and their early use of this very rigid style of mash flow is that in all fairness, every attack in the combo past the very first attack was just a satisfying formality; you could design the same game without even having combos. But they did it anyway because it was incredibly satisfying to players. So much, in fact, that we've been iterating on this basic formula for 25 years.
Type 2: Traditional
It didn't take very long for game designers to realize they were misusing an entire button with a trivial redundancy so they smashed the game's important mechanics into one button. Thanks to this decision, the second generation of beat 'em ups (Final Fight, Streets of Rage, Golden Axe, all the way up into the later era of Aliens Vs Predator, Battle Circuit, and Armored Warriors) were much more elegant and had the players navigating the game environment, staying clear of attacks, and then pinpointing the right moment in which to execute one very useful string of attacks by mashing one button. Eventually the genre developed a "special attack" button that would execute a unique mechanic that was very powerful but also very limited in use. Before the implementation of this ability on its own button, most beat 'em ups let players perform this by pushing the attack and jump buttons at the same time. This was too difficult for the average player to do reliably, hence the move to its own button.
Type 3: Gap Timed
One of many concepts the first Devil May Cry introduced into the world of beat 'em ups is the idea of branching live combos into completely different combos by waiting at key points in the combo for a split-second before hitting the attack button again. For example, pressing A four times in a row would get you a fundamental standing combo, but pushing A twice, waiting for the second attack animation to approach completion, and then pressing A two more times would get you a completely different combo. The benefit of this method of mashing is that it's varied but elegant. The downside is that most players struggle with the execution of this type of combo and give up on it, which is understandable.
Type 4: Circuit Jumping
Heavily popularized by Team Ninja's Ninja Gaiden and Sony Santa Monica's God of War, beat 'em ups eventually returned to a two-button input scheme that offered "light attack" functionality on one button and "heavy attack" functionality on the other. Admittedly, this can feel a lot like the Super Traditional mash flow but there are two key differences. The first key difference is that the attack types don't just look different, but they feel different and have different effects. For all intents and purposes, attacks on one button in Super Traditional mash flow games are functionally identical to attacks on the other button, they just look different. The other key difference is that modern beat 'em ups have formalized the dynamic use of the two buttons so that it is still considered one combo if the player decides to jump into the other circuit. This was certainly not the case in Super Traditional games, which is another reason the second button was ultimately useless. Circuit Jumping mash flow allows the player to switch mid-stream between the light and fast combo they have started to the slower and more powerful combo they want to finish with, or vice versa. Once they have jumped, however, they must follow through to the end of the new circuit.
Type 5: Super Flexible
This super modern and very newly employed mash flow is an incredibly flexible and intuitive flow that allows the player to switch back and forth between attacks types on two different buttons whenever they want as a dynamic response to whatever is happening around them. As far as I know, the only games that have implemented a mash flow like this are Bayonetta and Dante's Inferno. To be fair, Bayonetta is much more nuanced than this diagram would suggest, but for the most part the idea is on the mark. While it does have the potential to be very exciting and expressive, the danger with this mash flow (as evidenced by both Bayonetta and Dante's Inferno) is that your attacks can lose meaning. I say "danger" and not "problem" because I don't believe this issue is inherent to the flow type, but to the game. In Dante's Inferno, none of the standard attacks on these buttons are particularly meaningful or different from each other. In Bayonetta, the problem is fascinating; there is such a vast amount of meaningful attacks and combos that many of them are rendered meaningless by our human habit of "sticking to what works". I firmly believe this idea can be wrangled in to create something that feels dynamic but doesn't get turned to mush by the player's brain when they are knee-deep in an encounter.
I wrote this post to create new language. If you started using these terms to describe the types of combos you like and want to implement it would inject joy directly into my biological joy parser. :)