A lot, and it gets confusing.
A pistol can be legally converted into a rifle format (over 26" with 16"+ barrel), and then legally converted back into a pistol format (no vertical forward grip or butt stock, with no minimum overall or barrel length.)
A decision going back to the Thompson case, and which the ATF finally made official more recently.
A rifle can not be converted into a pistol format, even in legal pistol dimensions and with no stock it is a SBR and requires an NFA stamp.
What that means is that a pistol has the freedom to be both, and a rifle must remain a rifle.
So you could not legally use the lower from an AR-15 you purchased as a rifle.
That would be an unregistered SBR.
You could legally use the lower of an AR pistol, and you could also use just a plain lower of course then without the legal protection of being paperworked as a pistol (so what is it really then? Do you need to make it a pistol first to then make it a rifle that can legally go back to a pistol, or does it start legal to do both having been sold as a receiver?)
It still could not have a buttstock in a legal configuration as a pistol.
Now a 'permanently' attached muzzle break or flash hider that brought it over 16" could allow it to be used on a rifle.