IM platforms like Skype are peer-to-peer - this means when you call someone, your connection goes directly to the recipient's computer - there is no connection to Skype's servers in this process (well, there isn't a necessary connection).
IM platforms like Discord are not peer-to-peer - when you send a message, call someone, or do anything, your connection sends a message to Discord's servers, which is then relayed to whoever needs to see it.
Because Discord isn't peer-to-peer, it isn't possible for people to see your IP address when you send a message to them, call them, etc.. but is your IP address shared with the admins of Discord servers (the owners of servers you are in, not Discord employees)?
The answer is no - the only people who can see your IP address are Discord themselves, and your IP address is not shared by Discord, to anyone.
Whilst it may be obvious to some, it is important to note that if you visit an external link that was sent to you via Discord, the external site will be able to see your IP address. E.g. if someone sends you a link to google.com, Google will be able to see your IP address.
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