Is it a suppressor or a silencer? So what do you call the device used to reduce the report of a firearm? In terms of actual function, "suppressor" is a better term because "mufflers," as they are called in some parts of the world (where they can be purchased over the counter like a bipod) do not completely eliminate all the noise of firing. They do not render guns completely "silent" but they do drop the decibels down to a level that it does not damage human hearing.
So then, where did "silencer" come from? You can look to the guy who invented them: Hiram Percy Maxim. The son of machine-gun inventor Sir Hiram S. Maxim, Hiram P. Maxim formed the first successful suppressor commercial enterprise, named the Maxim Silencer Company.
His 1909 patent called it a silencer, too. Arms & The Man and then The American Rifleman was chock full of Maxim Silencer Co. ads. Even NRA Life member and U.S. President Theodore Roosevelt had a Maxim Silencer on his Winchester Model 94 in .30-30 Win. (it was the polite thing to do for your Oyster Bay neighbors).
But it was only partially commercial successful, and by the late 1920s, Maxim turned his inventing talent to lucratively silencing other loud things—such as large industrial machines. His Maxim Silencer Company is still in business today, but it does not make silencers (or suppressors for firearms). In homage to Hiram Percy, Silencerco named its integrally suppressed pistol the "Maxim 9." The suppressor in the image at top is the SilencerCo Osprey Micro, and is attached to the Browning Black Label 1911-22 A1 rimfire pistol.