muzzle brake - reduces felt recoil by directing muzzle gases back.
compensator - reduces muzzle flip by directing muzzle gases upward.
flash hider - prevents shooter from being blinded by muzzle flash in low-light conditions by shielding shooter's eyes from the muzzle flash.
flash suppressor - prevents shooter from being blinded by muzzle flash in low-light conditions, and reduces chance shooter will be spotted by an enemy in low-light conditions by reducing the overall flash at the muzzle.
First item shown by shivan - a phantom flash suppressor. Quite effective. Not a brake or compensator - just reduces muzzle flash and is not legal on a post-ban semi auto with a pistol grip and the ability to accept a detachable magazine.
"Mini Y-comp" - combination muzzle brake and compensator, but not a flash suppressor.
"GI cone-style flash hider" - flash hider, but not a brake, flash suppressor or compensator.
"AK-74 style brake" - muzzle brake and compensator, but not a flash suppressor or hider.
"AK slant comp" - compensator but not a muzzle brake, flash suppressor or flash hider.
"A1 GI birdcage suppressor" - flash suppressor but not a brake or compensator.
"A2 GI half-birdcage suppressor" - flash suppressor and compensator, but not a muzzle brake.
"Smith Enterprises Vortex flash suppressor" - arguably the most effective flash suppressor available, but not a brake or comp.