Yup, Rob basically covers it all.
I think some people see muzzle rise as recoil though also. this is incorrect though. I would describe muzzle rise as more of a side affect of recoil.
the barrel sits in line with the bcg and buffer assembly all above the shooters grip. when the rifle recoils, the grip is basically a pivot point causing the muzzle to rise instead of the whole rifle going straight back.
while most rifles are about the same in this, you can really see the difference in handguns. a handgun with a low bore axis, meaning the barrel being lower and closer to the firing hand, will have less muzzle rise and be quicker back on target than a handgun with a higher bore axis. the best example of this is a Chiappa Rhino versus a regular revolver. The Rhino's barrel lines up with the bottom of the cylinder instead of the top of the cylinder like most revolvers. There are other semi auto pistols out there currently being designed to have low bore axis.
with bore axis, think of a lever in physics. a higher bore axis acts like a longer lever making that barrel easier to move, while a lower bore axis acts like a short lever making it more difficult to move.
That's all fine and dandy with pistols, but in an AR you basically have the same bore axis no matter what. So how do you try and limit muzzle rise since you can't change the bore axis? Weight and gas management.
With weight, if you are front end heavy, this will help with muzzle rise because takes more force to make the heavy front rise in the first place. Now this is often times seen in long range bolt actions, but probably not the best idea for an already heavy 308AR platform. You would have to add a good couple of pounds to the front, which would quickly turn your rifle in to a 12+ pound rifle. and being front heavy, it would be exhausting to carry and shoulder for any period of time.
The best bet these days to deal with muzzle rise is gas management. And I am talking about how the gas is directed as it exits the barrel. Compensators have long been used to tame muzzle rise, as the barrel wants to rise up, direct the gas to give it some force back down. A simple concept of thrust. Now with many designs the downside is you have gasses going up into the line of sight of your optics or sights, which can affect follow up shots. Luckily these days many good muzzle brakes have compensator slots or holes in them in different directions to prevent all the gasses from going up where you don't want them. I recently purchased one of many such items, a VG6 Precision brake. With this one, the majority of the gasses are directed out the sides, helping with the felt recoil, while a small amount goes through slits in the top to help tame muzzle rise. but even by limiting that felt recoil wanting to push back against that pivot point, that also helps with the muzzle rise remember. 😉