'If your AR was originally a Pistol you could interchange uppers, but if your AR was originally a rifle.....putting a short upper on it is illegal, unless you pay the tax and get it registered as a SBR. ' True but!
Can be 'other' or 'pistol', with buffer tube or brace ONLY. Also must be under 26" overall length (? collapsible brace collapsed). If getting one, fill out the form as pistol. Not all braces have a BATF 'letter' but this is being worked on IIRC. There are folding stocks, folding buffer tubes and other options out there, that could get dicey. Wildest one I've seen is a 5" barrel, 2" buffer tube, custom BGC in 223. Some have also gone AK style.
AR's trigger group being sold (registered?) ?? FA trigger group is a real expensive alternate!! BGC are sold as SA/FA variants but I've not seen any legal distinction.
Many bare lowers were sold as 'other' and can be either but once 'configured' they are pistol or rifle. Meant to be for bare actions, etc and very dubious definition. So basically stay away from it - was primarily for manufacturers/builders.