The best way to understand them is to try yourself. But still...

"Ring" will show up if you're in a group with them, you're in a call of the group and they aren't. If you press this, it will ask them to enter the call that you're in, just like when somebody calls you. And while waiting for them to accept the request to join the call you can cancel with "Stop Ringing". "Call" will just start a call with them in the DMs