Fair warning, I'm not a lawyer, so if you have questions, go get a real member of the BAR.
Whether silencers are considered firearms may just be splitting hairs, but if you refer to this Alphabet org publication:
https://www.Alphabet org.gov/firearms/docs/guide/Alphabet org-guidebook-importation-verification-firearms-ammunition-and-implements-war/download
Page 6:
NFA Firearms – Those firearms as defined in 26 U.S.C. § 5845, which include such firearms as machineguns, machinegun receivers,
silencers, short barreled rifles, short barreled shotguns, destructive devices, smoothbore pistols, and certain other firearms (including certain unserviceable weapons).
Yeah, silencers are in the same class as machine guns. Who'd have thought? Sometimes, Politicians aren't the brightest bulbs.
I think that just underscores how important it is to take proper care when purchasing a silencer (Moderator in our lingo), as the BATF considers silencers that can be used on firearms as an NFA firearm. Bizarre, but like I said, even in 1934, politicians didn't understand guns.
Now, the legality and how far the Feds can stretch the definition is limited. This case was mentioned in other posts here on AGN:
https://caselaw.findlaw.com/us-1st-circuit/1527670.html. The case shows the courts won't allow the BATF to just throw the book at people, but imagine paying your lawyer to get you off a Federal charge like that. It'd be really expensive, probably cost you jobs, and much more.
What it comes down to is that silencer law is murky at best. Lines are blurred, If you intend to build your own, get legal advice and a letter from the BATF, or just do it the easy way and buy one from a reputable dealer where the supplier already went through the legal hassles.
Also, as for state law, yes that varies by state. I live out west (not California, Washington or Oregon), and most Western states out here don't give a hoot about airguns, silencers or anything related. Do check your local state laws as NY, CA, NJ, Illinois and others can be pretty touchy about anything gun related including airguns.