You can set Firefox to update automatically.
If you have a version of Firefox installed, and then download a different version, then the new version will not get installed in the same location--unless you do it overtly. What I typically do is put all downloaded SW (ie anything not gotten thru the package manager) in /opt. then simply edit the appropriate menu item or launcher to point to the new version.
NOTE: What you download from the Firefox site is not an update--it is the complete program.