But yes, some DD's are off limits. Try and buy a frag grenade or HE rounds for a .50 BMG and see what I mean.
Some SBS (Short Barreled Shotguns) are DD's that you can put on a Form 4. Certain "street sweepers", or other short length shotguns, are NFA restricted and good luck getting the BATFE to sign off on your forms.
SBR's just need the right paperwork filled out, the right palms greased, and the receiver engraved.
For DD's and AOW's, it's pretty much up to the BATFE's arbitray BS whether or not they want to sign off on it.
Contrast this to my point that none of these arbitrary classifications should exist at all.
Nope, it's still all available ('cept post-'86 MGs). You can get the go-boom stuff, it's just that you have to pay the $200 tax on each round. Ok, so that turns in to a practical ban...which was the point of NFA in the first place (ex.: $200 tax on a $5 MG in 1935). Only reason we tolerate NFA now is that inflation over 70+ years has brought the value of $200 down to a tolerable tax on good quality stuff (and comparably, the taxed stuff has risen in quality to warrant such prices - suppressors shouldn't be $1000, but if you're going to pay $200 tax on one you might as well get something really quiet and indestructable). If the tax had been indexed to inflation, we'd have gotten a case to SCOTUS overturning NFA already.