Rookie question but just want to be sure - there are no restrictions of buying / shipping parts like barrels / stocks / etc. as long as they are not FFL required parts correct?

No serial # ..... not a gun

Some barrels (Ruger Mark series of pistols comes to mind) are serialed receivers and therefore require an FFL.

 

Tho an XD barrel has a serial, it is not a considered a "gun" or receiver.

 

So, serial number alone is not an indication.

 

But in most cases 67GTO is correct.

The receiver is teh part that is serial numbered and is considered the firearm in the US. Many countries consider the barrel the firearm that's why Glocks and others have serial numbers on the barrel.