I call them circle spawners. The enemies spawn in a rough circle around you and close in. I think you can modify that with other terms depending on the specifics of what the game adds in.

I think my favorite couch coop game was Resistance on playstation 3. Some friends had it and we spent an entire week blasting through the game. It had a lot of potential for fun, like when I meleed the enemy in the face, then my friend with a sniper rifle slowed time, aimed between my character’s arms for the recoiling head of the enemy and got the headshot.

The problem with the first (I haven’t played the second), was that it felt like a story game where you play through the story in one go, when it ultimately turned out to be an instance grinding game to get gear to progress.

I went in expecting dark souls with guns, but got the weird love child of world of warcraft and dark souls with a reset button to progress.