See https://malwaretips.com/blogs/safesearch-net-removal/

If you get a pop-up message asking to update Firefox or plugins or scanning for malware then such a message is likely a scam and you should never respond to such an alert to avoid getting infected with malware.

• Only update Firefox via "Help > About" or by downloading and installing Firefox from the Mozilla server and never via a pop-up or link on a web page.
• plugins should only be updated via the plugin itself or by visiting the home page of the plugin.

You can find the full version of the current Firefox release (47.0) in all languages and all operating systems here:

• https://www.mozilla.org/en-US/firefox/all/

I downloaded this off the Mozilla website. It was supposed to be the legitimate version. When I log in on the website it says I have the newest version. It's the name that is throwing me, Safesearch.

I downloaded this from the Mozilla website. It was supposed to be the newest version but it is called safesearch and that has me confused. When I log onto Mozilla I am informed that I have the newest version but it does not say Firefox. Has the name changed?

The web browser is still Mozilla Firefox or Firefox for short. Mozilla has no intention of changing the name of this web browser again since it was changed to name of Firefox for version 0.8 way back in February, 2004.

Something on your Windows installed this Safesearch hijacker into Firefox as it does Not come with Firefox for Windows, Mac OSX, Linux from www.mozilla.org or www.mozilla.org/firefox/all/

See the first link posted by cor-el above.

You have to be careful when downloading applications for Windows as some download websites may bundle stuff with otherwise clean applications. One that has been guilty of doing that is cnet aka download .com