I've seen ads for both; and some of them look the same...

What is the difference between a birdcage flash hider and what looks like a birdcage flash hider but is labeled as a muzzle brake???

Is there something simple that I'm missing here???

On a postban rifle? 10 yrs in the federal prison system..[:D] Sorry, couldn't help myself

Who Cares?

Actually its the machining cuts made in the metal.  One is evil one is good!

Muzzle break deflects gasses to the side and rear to force the weapon forward and reduce recoil. This is usually annoying to VERY annoying for people to your left and right at the range. A flash hider is usually a conical attachment for the muzzle to cover any muzzle flash. A flash suppressor is an attachment at the muzzle to dissipate the hot and oxygen deficient gasses so that they do not mix with the air and reignite causing muzzle flash. You asked for two and here you get three definitions.

Functionally, if it measurably reduces the flash signature of the weapon from downrange, then it's a flash suppressor.

If it helps counteract recoil, it's a muzzle brake.

If it helps counteract muzzle rise, then it's a compensator.

Many devices are a combination of two or more of those characteristics.  To be post-ban legal, it cannot reduce flash, although it can function as both a brake and a compensator.

Don't confuse flash suppressor (which reduces flash) with flash hider (shields your eyes from the flash).  Something like a WW2 conical flash hider doesn't reduce the flash signature downrange at all, and is legal on a postban AR-15 (although not in a standard threading also used for flash suppressors), while a flash suppressor is not, generally.

Sorry; I guess I was too ambiguous here...

What I meant to say was, if the two look alike, what is the difference, physically???

If one site has a "birdcage" advertised as a FH, and another has a seemingly identical "birdcage" advertised as a MB, what part of the machining makes them different???

The size of the opening at the business end of the FS/MB.  A muzzle brake has an opening sized just over the size of the bore (similar to a compensator) while a flash suppressor is fully opened at the muzzle.

HTH!

Ah; OK...I didn't notice that...

Thanks for the info!

I suppose the muzzle brake, if installed on a post-ban, has to be permanently mounted, is that correct? Either pinned or silver-soldered?

yes, and the pin holes have to be welded.
Ar's don't really a brake, and they're really LOUD. Better to get a fake FH,and,yes, it will have to be "permenant" as well. [;)]