More specifically, the part that is classified as a firearm. VP9's have the barrel serialized and you don't need a FFL to bring in the barrel. SIG P320 is the fire control unit and not the frame of the gun is the serialized part and the part that's considered the firearm.
A barrel is not a frame or receiver. So that part doesn't qualify as the "firearm" whether or not it's serialized.
I think the more correct answer is the part of the gun that houses the trigger control group (TCG) is the part that requires an FFL.
If you're struggling with these definitions for a "firearm", you're not alone. The ATF is struggling, too. Every time they make a definition too specific, new designs and technical changes make the definitions inapplicable. The ATF likes to use industry standards when they define something, but there are many examples of nonstandard firearm designs that conflict with those definitions.
The AR-15 is made up of 2 separable receivers. The lower receiver has been viewed for decades as the "firearm" requiring FFL controls. However, the ATF definitions include characteristics like "contains the firing pin" which applies to the upper. Because the definitions are ambiguous, and even the ATF doesn't require uppers to be controlled, they are fumbling in court when someone manufactures a receiver as the current definition excludes 2-part receivers that house different components of the firearm.
If you want to read up on the latest ATF info on this, go here:
https://www.federalregister.gov/documents/2022/04/26/2022-08026/definition-of-frame-or-receiver-and-identification-of-firearmsAnyway, the best way to tell if a part needs an FFL is to go online and try to order one. If the site requests an FFL at check-out, then it's a controlled item. If not, it's legal to ship to you directly.You're still allowed to buy P80 80% receivers here, but they have to be serialized by the seller and handled by a local FFL, even though they are not, by ATF definition, firearms.