Matrix is an interoperability protocol (like activityPub, which mastodon, friendica, Lemmy, pixelfed etc… all use to communicate with one another) rather than the actual application being used.
The UI you’re describing is probably Element, which is the most common matrix implementation used, though others do exist. A good example is probably rocket.chat; they’ve leaned harder into the discord like feel, whilst making use of the matrix protocol.
As for Stoat chat; It’s a rebrand of revolt chat, who have previously resisted calls for federation due to the perceived complexity of implementing (or creating their own i guess) protocol. That’s not to say it doesn’t have it’s uses; but it would be silly to assume people won’t try to steer you towards federated services on the fediverse 😉 and stoat don’t seem to have changed their stance on the matter.
Someone mentioned commet as a discord like matrix client the other day. I’ve trialled it using my matrix setup, and it looks and feels very clean, I definitely prefer it to element.
Unfortunately as the tale always goes, it’s not quite on par with element in features (it claims to have RTC support using livekit, but I couldn’t find the group call option), but it’s definitely one of the more interesting clients to come about recently. I really like the separation of spaces and personal chats, and the multiple accounts feature is useful from a sysadmin perspective.
Once they manage voice channels with RTC, I think matrix will finally have its discord alternative that could see some adoption with everyday users.