A flash suppressor works by providing a visual shield extending from the muzzle of the gun to mask the flash from burning exhaust gases. Some provide expansion chambers that increase their efficiency somewhat by delaying the escape of some of the gas and cooling it by expansion and mixing with air. A "silencer" is a particularly efficient form of flash suppressor.
A muzzle brake (or compensator) is anything that slows muzzle rise. That includes simple (or not so simple) weights, and gas deflection schemes that divert gas upward. Weights work under all circumstances, whereas various means of deflecting gas work best with some determined volume and velocity of gas.
Porting is the science of venting gas for the purpose of cancelling the various contributions to the motion of the gun. The ports tend to work best with a narrow range of loads with any particular gun.
The terms suppressor, muzzle brake, and compensator as commonly used overlap considerably.
In general, anything that puts weight out front and as far from the axis of the barrel as possible acts to control muzzle rise and other motion in proportion to it's weight. Controlling motion imparted by the shooter is arguably of more importance than controlling rise.
yes a muzzle brake will reduce felt recoil. i know 5.56 hardly has any but i put a alg defense on my 1st ar and a miculek type brake on my 2nd and there is a noticeable difference in rise and felt recoil. now that said if you are bench shooting and there is anyone near you and you have a really good brake everyone near you is going to hate you as it sends that blast out sideways and others have to deal with your reduced felt recoil.