I'm a very new drummer and curious how people learned new beats. At first I would get a feel for the beat and play but then I realized that reading the music quickly is important if the teach says: "Play this one". So I'm curious do you just feel the beat or do you read/play the musical notation?
Combination. Early on I read and count but after a billion repetitions it becomes internal. I usually look for something similar to something I've played before so I'm learning it as a variation of something I already know. Or I try and shortcut it by figuring out the phrasing, which for me can frequently burn something into memory quickly. To me, it's the difference between reading from a script and capturing the nuance of emotion in the words that comes with practice.
Though, of course, at a high level you should pretty much be able to capture the nuance at first read, but I readily admit my reading skills aren't to that level yet. I'm still in the sounding-stuff-out phase.