A muzzle brake, and I'm so glad you you didn't spell it b-r-e-a-k, reduces recoil. Many of them spew gas in all directions radially. A compensator reduces muzzle climb, usually by having ports facing straight up, diagonally up to the left and right, or in all three directions. Think of a ported barrel and it's similar in concept. A flash suppressor does what the name implies. Many muzzle devices function as 2 out 3 things, like when they closed the bottom of the birdcage on the A1 flash suppressor and it became the A2 compensator for whatever good it did. And sometimes you can find one device that functions as all three, muzzle brake, compensator, and flash hider. The old Fabian Brothers DTA Mil-Brake on my 20" AR barrel does it all. My 16" barrel has a slip-over fake suppressor on it that makes it look like a 10" barrel and has nothing added to the muzzle at all but I have an A2 birdcage for it. I want to keep the length short but flash suppression effective enough to shoot at night without impairing my night vision. You never know when some mangy varmint might need to be shot.
I don't have that upper on a lower now and I haven't shot a 16" AR without a flash suppressor at night. But a shot right in front of me with my dad's 18 1/2" Mini-14 temporarily blinded me. When I could see again I was seeing spots for awhile after that. That was after I shot my AR with the DTA Mil-Brake on the 16" barrel with a round from the same box. I think maybe there was a flash but dimmer than a firefly in the distance. I can't remember if it was next to nothing, or nothing at all. The majority of rifle and pistol muzzle brakes I've seen have small ports straight to the sides, plus a big port or ports on top, technically making them more of a compensator than a muzzle brake. But they can call it whatever they want as long as they don't call it a muzzle break. If it's going to break my muzzle I don't want anything to do with it. And if they're too stupid to know the difference between brake and break, I don't have much faith in their ability to design, test, and prove the effectiveness of their "break".