Community Managers deal with bans, silences, name changes and pretty much everything that has to do with the community.
They take care of our Discord server and reply to emails sent to the support services (email and support.i-need-to.click). Community Managers have a red name in the in-game chat.
Developers add new features to the server, squash bugs, keep the server up and running and take care of its maintenance.
They don't do anything related to the community. Developers have a blue name in the in-game chat.
Chat moderators manage the chat to make sure The Law™ (the rules) is respected.
BATs play beatmaps in the ranking queue and decide whether they are good enough to be ranked or not.
Here's a list of people who helped with Ripple.