The Maxim Silencer was the first commercially successful firearm sound suppressor. Developed by Hiram Percy Maxim (son of Sir Hiram Stevens Maxim, who invented the Maxim machine gun) in tandem with the automobile muffler in the early 1900s, it was patented in 1909.
https://www.forgottenweapons.com/accessories/maxim-silencer/
I ended up going down a wikipedia hole because I was curious about the inventor also making a car muffler, and it looks like it might be a regional thing. Sort of. Like, we’re trying to make it one.
Originally, everyone called them silencers, but apparently “suppressor” started to gain traction in the US in the late '80s. Since then, most American firearms groups have picked up the newer term, including the ASA (formerly American Silencer Association, now American Suppressor Association); meanwhile Britain is starting to adopt the term “sound moderator.” Neither term is really wrong, per se, it’s mainly a matter of preference.
As a side note, it turns out that Maxim’s company is still around! It looks like they only make the boring kind of silencer, though.