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Any rifle with a barrel under 16" with a stock, fixed or otherwise, would constitute an SBR and requires going through the process of registration and tax stamp. It's an NFA item. You can't just build it without breaking federal law. Read and read some more. Plenty helpful guides here and elsewhere. You don't want to screw this up.
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This.
If it has a stock, it is a rifle.If it has a stock and a barrel 16" or greater (and 26" or greater in overall length) it is a title 1 rifle, legal to own under the most basic laws, no additional regulations.
If it has a stock and a barrel less than 16" or is less than 26" in overall length, then it is a title 2 rifle, AKA a short-barreled rifle and is regulated by the National Firearms Act (NFA). Before you can build or posses an NFA weapon, you must submit paperwork to the ATF, pay a tax of $200, and await their approval. At that point the weapon is then registered with the federal government and has a few additional regulations tied to it.
An AR configured as a pistol has no stock. There are no other limits on the maximum or minimum barrel length or overall length of a pistol. Pistols are title 1 weapons, and are legal to own under the most basic laws, no additional regulations.
One additional rule is that a pistol, by definition cannot have a vertical for grip.
Now it gets a bit more involved.
If you have a pistol,
and it is
less than 26" in overall length,
and you attach a VFG, you will have re-made the weapon into an Any-Other-Weapon, which is a title 2 NFA regulated item requiring the same additional consideration mentioned above as for a short-barreled rifle.
If you have a pistol,
and it is
equal to or greater than than 26" in overall length,
and you attach a VFG, you will have re-made the weapon into a title 1 "firearm". Like the tile 1 rifle, it is legal to own under the most basic laws, no additional regulations.
All of the above pertains to federal laws only, some states and localities have stricter or additional laws. However, if you are in Ohio as your profile says, than know that there are no OH state laws that add to the above.