If you are wondering what your default web browser is set to on a Debian-based system, there are several things to look at:

$ xdg-settings get default-web-browser
brave-browser.desktop

$ xdg-mime query default x-scheme-handler/http
brave-browser.desktop

$ xdg-mime query default x-scheme-handler/https
brave-browser.desktop

$ ls -l /etc/alternatives/x-www-browser
lrwxrwxrwx 1 root root 29 Jul  5  2019 /etc/alternatives/x-www-browser -> /usr/bin/brave-browser-stable*

$ ls -l /etc/alternatives/gnome-www-browser
lrwxrwxrwx 1 root root 29 Jul  5  2019 /etc/alternatives/gnome-www-browser -> /usr/bin/brave-browser-stable*

Debian-specific tools

The contents of /etc/alternatives/ is system-wide defaults and must therefore be set as root:

sudo update-alternatives --config x-www-browser
sudo update-alternatives --config gnome-www-browser

The sensible-browser tool (from the sensible-utils package) will use these to automatically launch the most appropriate web browser depending on the desktop environment.

Standard MIME tools

The others can be changed as a normal user. Using xdg-settings:

xdg-settings set default-web-browser brave-browser-beta.desktop

will also change what the two xdg-mime commands return:

$ xdg-mime query default x-scheme-handler/http
brave-browser-beta.desktop

$ xdg-mime query default x-scheme-handler/https
brave-browser-beta.desktop

since it puts the following in ~/.config/mimeapps.list:

[Default Applications]
text/html=brave-browser-beta.desktop
x-scheme-handler/http=brave-browser-beta.desktop
x-scheme-handler/https=brave-browser-beta.desktop
x-scheme-handler/about=brave-browser-beta.desktop
x-scheme-handler/unknown=brave-browser-beta.desktop

Note that if you delete these entries, then the system-wide defaults, defined in /etc/mailcap, will be used, as provided by the mime-support package.

Changing the x-scheme-handler/http (or x-scheme-handler/https) association directly using:

xdg-mime default brave-browser-nightly.desktop x-scheme-handler/http

will only change that particular one. I suppose this means you could have one browser for insecure HTTP sites (hopefully with HTTPS Everywhere installed) and one for HTTPS sites though I'm not sure why anybody would want that.

Summary

In short, if you want to set your default browser everywhere (using Brave in this example), do the following:

sudo update-alternatives --config x-www-browser
sudo update-alternatives --config gnome-www-browser
xdg-settings set default-web-browser brave-browser.desktop