Thanks. It's slightly worse than I thought. I'm kinda limited to communication with my small peer group, so I don't notice that other user classes exist.
Matrix works a little like email, but instantaneous and secure:
You need to register an account at a provider
Whatever your provider is, you can talk to people using other providers
In the same way you can use Outlook or Thunderbird with the same email account, you can use different Matrix apps for the same Matrix account.
Several apps exist, but we're going to go with Element for the sake of simplicity, as it's among the most fully-featured Matrix apps on the market.
Once you are more comfortable with the basics and if you want to use another app, head to the clients section of this website.