Matrix is the protocol, Element is one of the messaging clients that uses it.

I don't think matrix supports game streaming. revolt voice chat didn't even work for me, which made sense because it had a big "warning, this is deprecated, a replacement is being worked on". Don't know if they finished it. Never heard of guilded.

Discord has a nice UI and lots of neat features, and it's popular among gamers especially, but it can hardly be recommended. See https://www.messenger-matrix.de/messenger-matrix-en.html for a comparison with other communication programs. Yes, Discord has approximately the most red flags there can be. Discord is essentially spyware, it supports the least amount of encryption, security and privacy techniques out of them all, and everything you type, write, say and show on it is being processed and analyzed by the Discord server and probably in turn sold to 3rd parties. Discord can't make a living from selling paid features only, they have to sell tons of user data, and since all data is basically unencrypted, everything's free for the taking. Discord doesn't even try to hide it in the terms of service or so. They just plainly state they're collecting everything. Well, at least they're honest about it. It's a minor plus. If I had to use Discord, I'd only ever use the web browser version, and I'd at least block its API endpoints for collecting random telemetry and typing data (it doesn't only collect what you sent, it also collects what you started typing).

Matrix, on the other hand, is a protocol. Element is a well-known Matrix client implementing the protocol. On Matrix, everything is encrypted using quite state of the art encryption. It's technologically much more advanced than Discord is. It's also similar, but it won't reach feature parity with Discord. Discord is a much faster moving target, and it's much easier for the Discord devs because they need to, oh, take care of exactly nothing while developing it further. While adding a new feature to Matrix is much more complicated because almost everything has to be encrypted and still work for the users inside the chat channels.

This is just broadly written for context. The two are similar, and you should prefer Matrix whenever possible, but I do get that Discord is popular and as is the case with popular social media or communication tools, at some point you have to bite the bullet when you don't want to be left out of something. I'm just urging everyone to keep their communication and usage on Discord to an absolute minimum, never install any locally running software from them (maybe using sandboxing), and when you're chatting or talking on Discord, try to restrict yourself to the topics at hand (probably gaming) and don't discuss anything else there. Discord is, by all measurements I know, the worst privacy offender I can think about. Even worse than Facebook Messenger, WhatsApp and such stuff, because they at least have some form of data protection implemented, even if they also collect a lot of stuff, especially all metadata.