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Been thinking about it again, and the org's FAQs are way too technical for me to understand, so can someone explain me simply how Matrix actually works?

I understand that you need to pick a home server for your account, but it's like, not like a Fediverse instance where other users on the server can just start chatting right? You need to have somebody's direct username to start an interaction, or be invited into a room. Is that right?

I feel like there's a few people I would like to have more private chat with but I know a lot of people are avoiding Discord; this is why I ask.