From what I recall a 'firearm' is a legal word of art for a receiver or frame registered with the BATF for sale through a FFL licensed dealer. Everything else that attaches to the receiver isn't the 'firearm', its the receiver. Its the receiver that is registered 'in commerce' and called a 'firearm'. They don't use the word 'gun' or 'arm by itself. The receiver 'carries' (a commercial term) the parts. So technically the idea of 'firearm' parts might be a misnomer in legalese with the notion of the frame or receiver being the firearm.
Related:Q&A With "Allodial"
Q. What part of a a gun bears the serial number? A. The receiver or the frame.
Q. According to U.S. laws or regulations, what part of a gun is the firearm? A. The receiver or the frame. (It is the 'controlled part'.)
Q. Are there any guns that have more than one frame or receiver? A. Yes. An AR-15 has an upper receiver and a lower receiver. (The lower is typically serialized).
What's the Marking On A Frame or Receiver?