When I’m asked in my messages to join in, are they proposing that I join a group or are they referring me to sing a certain song or both?

[[Member Crai…]]

If asked for a join on my private messaging are they referring to me joining a group or asking me to sing with them?

[[Member open…]]

You probably mean something like this:

That’s a message invite to sing that particular song with them. It’s the same invite that usually goes out to all followers, but one can also send it to selected people as a message.