Here is the legal differences of the two and why:
When the 1934 NFA was being crafted, along with fully automatic firearms, they wanted to restrict handguns as well. Basically anything easily concealable they wanted to add to the NFA registry. They crafted language to include Short Barreled Rifles (SBR) and Short Barreled Shotguns (SBS), setting minimums for both barrel sizes and overall length. This would prevent people from working around the restrictions, and making their rifle or shot gun too short easier to conceal.
The language for restricting handguns was dropped from the NFA, but the SBR and SBS language was left in. In most states you can still get an SBR or SBS, you can even build one yourself, but you have to register it with the ATF, pay a $200 tax, and wait 6-9months on average for a background check.
Before 2013, if you wanted a super short AR, you bought a “pistol”, which is very short AR with no stock, but the needed buffer tube sticking out.(See the top part of the pic below.) Even though I used quotes around pistol, these are classified federally as pistols and thus fall under the same restrictions of other handguns (must be over 21,etc).
In 2013 Sig Sauer came out with the Sig Brace (See the bottom part of the pic). This was a device designed to wrap around the forearm and help brace the pistol for one handed shooting. The ATF approved the device. People then of course asked the question, “What if I put this on my shoulder and use it as a stock?” And after a bit of waffling, the ATF concluded that if the device was designed and approved to be used as a brace, then it is a pistol brace, even if there was “incidental use” of it as a shoulder stock. Basically they can’t stop you from using it wrong.
So, since then several more companies make similar braces, most of them approved by the ATF, and the ATF more or less made the SBR designation redundant.
So the reason for the top item is it is $200 cheaper and you don’t have to wait 6-9months to own one.
I don’t think its classification as a pistol would matter in regards to being able to legally conceal carry it. I am not aware of a state that has language that allows CCW, but does not allow that weapon to be a rifle. I could be wrong on that.
Some of you may be pleased to know that the legality of that brace could literally change overnight with the ATF changing their decision on the matter and saying adding a brace to your pistol would make it an SBR. This is what happened with the “bump stocks” under Trump. Anyone owning one would have to remove it, and then register their lower as an SBR if they wanted to add it or a regular stock back on.