Mozilla does not have a search engine. We are an independent company, but default search features on the browser utilize Google. You can adjust your default search engine in settings by clicking the menu bar -> Options -> Search

See also https://support.mozilla.org/en-US/kb/change-your-default-search-settings-firefox

Firefox is a web browser.

Are you a google related company? or is Firefox/Moz://a" an independent company?

As Eve already mentioned "an independent company", but in the USA Google is the default search engine. Other localized versions (i.e., different countries with predominate non-English language users) may have a different default search browser.

And as the hyperlink that James posted explains in detail, setting your own "default search engine" is easy to do. Also mentioned by Eve.

since Firefox 57.0 https://blog.mozilla.org/blog/2017/11/14/firefox-features-google-as-default-search-provider-in-the-u-s-canada-hong-kong-and-taiwan/