If I say silencer and someone corrects me and says it's a suppressor, I tell them that the inventor, Hiram Percy Maxim called it a silencer, and that's good enough for me. You can't argue with the inventor what his invention is called. He also invented the car muffler, and if gun laws were anything like car laws, every gun would be required to have a silencer, AKA muffler when you buy it. The ATF calls them silencers, and mufflers too, but mufflers is an old term that's very uncommon nowadays.
Gun Control Act Definitions
Silencer
18 U.S.C., § 921(A)(24)
The term “Firearm Silencer” or “Firearm Muffler” means any device for silencing, muffling, or diminishing the report of a portable firearm, including any combination of parts, designed or redesigned, and intended for the use in assembling or fabricating a firearm silencer or firearm muffler, any part intended only for use in such assembly or fabrication.