Supposedly, activity.
But the definition of activity seems pretty odd to me. Playing in a team match (even registering for one, I think) doesn't count. So a quiet member who doesn't read a group's forums or notes, or post in them, but joins matches when they get a PM can (I think) get stuck in "all_time".
I'm really more interested in when someone last played in a match or posted and/or voted in a team match game. People who do those things but don't post or look at the team's main notes page are common in my experience.
I simply jam all members together and if I want to know when someone was last online, that's their profile. The last time they played one of our matches? That's painful unless the matches are cached and you have player_id for everyone to sort out name changes. (I don't have all this stuff; one day, I hope.)
Vote chess? No endpoints. I hope that's "No endpoints, yet" but we'll see.
"Try adding all_time, monthly and weekly together" - I haven't needed to use the club endpoint yet but what's the distinction between these different sets of members?
When I use the Manage Members facility as an admin in one of my groups, I don't see the same headings, members are simply members.