My latest "American Rifleman" has a ad for "The new Sig MP available in 3 configurations." Carbine (simple enough) SMG (I imagine sub machine gun) and SBR. SBR? The only thing that seems to make sense is "short barreled rifle". But isn't that a carbine?

No, that would be less than 16". The carbine could run from 16" to maybe20" depending on model.

If the barrel is less than 16", you need a form1 and a ($200) tax stamp. They are backed up almost a year now. Don't even have the parts around until your tax stamp is in your hot little hand.
There should be some good information in the legal & RKBA section.

Wiki says it is short barreled rifle, a legal term for <16".

Yes. Short Barreled Rifle is the legal name for a rifle that has a barrel less than 16 inches in length, OR an overall length of less than 26 inches, or both.

There is a similar legal name - Short Barreled Shotgun - which is a shotgun with a barrel less than 18 inches or an overall length of less than 26 inches, or both.

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I always take precautions

the really fun one would be the subgun in 357 sig.

Sounds interesting. Any more information on these?