Both are scripts that, when configured by update-alternatives, call the default application for internet browsing on a GUI environment.
The script x-www-browser calls the application configured to run on any desktop environment that runs under X Server, while gnome-www-browser application configured specifically calls for GNOME. Similarly, www-browser is a script to call the default browser on a TUI (text-based user interface) environment, such as w3m or elinks, for example.
You can check which browser they are associated with the commands
sudo update-alternatives --display x-www-browser
and
sudo update-alternatives --display gnome-www-browser
To list all the alternatives to these scripts, use
sudo update-alternatives --list x-www-browser
and
sudo update-alternatives --list gnome-www-browser
To configure a default browser, use the commands
sudo update-alternatives --config x-www-browser
and
sudo update-alternatives --config gnome-www-browser
Since these scripts can call different browsers, it may happen that a certain program call a browser other than the default browser. This often causes confusion for some users, but this issue can be fixed by running the command sudo update-alternatives --config as explained in item 3, above.
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