What is the difference between mute and block?

Mute: The connection stays in your list, but you no longer receive notifications from that user, and they cannot invite you to tournaments (if they try, they'll see that you've muted them). Useful if you want to keep the connection without getting their messages or invites.

Block: The user is removed from your saved list and hidden from search. They cannot add you again until you unblock them. Blocked users appear in Account → Connections under the "Blocked" tab where you can unblock them if you change your mind.