From NYS Penal Code Section 265.00 - Definitions:
22. "Assault weapon" means
(a) a semiautomatic rifle that has an ability to accept a detachable magazine and has at least one of the following characteristics:
(i) a folding or telescoping stock;
(ii) a pistol grip that protrudes conspicuously beneath the action of the weapon;
(iii) a thumbhole stock;
(iv) a second handgrip or a protruding grip that can be held by the non-trigger hand;
(v) a bayonet mount;
(vi) a flash suppressor, muzzle break, muzzle compensator, or threaded barrel designed to accommodate a flash suppressor, muzzle break, or muzzle compensator;
(vii) a grenade launcher;
Emphasis mine. I'm just saying that if I had to go to court to explain why I didn't have an SBR and just a pistol, it would be easier for me to argue that my foregrip is not a vertical foregrip if the name were different, rather than getting out a protractor.
In regards to the name of things, there's a reason why "pistol braces" exist that look like the SBA3 and SBA4: https://princelaw.files.wordpress.com/2019/07/atf-folded-brace_redacted.pdf