search engine

Yes because they call their web browser as Google Chrome or Chrome for short and not as Google which most may think of as the Google search engine.. Mozilla Firefox is the full name as Firefox is the short name yet many newer/less technical Firefox users mistakenly refer to the Firefox web browser as Mozilla. They also do this with Thunderbird as referring to Mozilla Thunderbird as Mozilla. So many people also mistakenly think Firefox is a search engine and not as a web browser. One could call the search engine with a full name of say "Firefox Search". However as I pointed out so many newer or less technical users will then very likely refer to both web browser and search engine as Firefox as if they were the same and not separate things. A name like "Mozilla Search" could perhaps be a better name to differentiate between the Firefox web browsers and search engine. However again people will perhaps mix up Mozilla Search with Mozilla Firefox in referring to as Mozilla. Mozilla does have a number of current and discontinued products with Firefox in name however they had another word(s) with it like Firefox Focus, Firefox Relay, FirefoxOS, FirefoxOS Marketplace, Firefox Private Network, Firefox Lockwise, Firefox Hello, Firefox Rocket/Lite, Firefox for Amazon Fire TV. Firefox Notes, Firefox Send. I have seen very few people mistake any of these as the regular Firefox web browser for desktop or Android/iOS/iPadOS. Btw Firefox Private Network was a subscription based product that worked much the same way the [https://support.mozilla.org/en-US/kb/built-in-vpn built-in VPN in desktop Firefox] and more recently in Firefox for Android works. It routes the browser traffic through proxy servers and neither is/were a full VPN like [https://vpn.mozilla.org Mozilla VPN] is. If Mozilla did not have this product they could have referred to the built-in VPN in Firefox as Firefox Private Network or FPN. Some newer/less technical users mistakenly refer to the built-in VPN as Firefox VPN (as if it was a standalone product) or Mozilla VPN (which is standalone) quite often actually. So short version is it would perhaps not be a good idea for Mozilla to refer to their search engine site as Firefox or Firefox Search.