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/
In reality they’re just interchangeable terms. Suppressor is increasingly popular because the term silencer can be seen as misleading (as it doesn’t make them silent just less loud). IMO use either or both, people will know what you’re talking about either way.