Services is great for when you need to know exactly who is going to show up on a specific date, and if they can't, you can find someone else to take their place.
Groups is great for situations where everyone in the group is always invited to each event or included in all communication.
If your people serve at an event, create the teams and positions in Services and add them to the plan they're serving in.
You can create templates of rotations or add needed positions to plans to schedule your team members.
If your people meet at times that don't coincide with service times, they'd be great groups. Create a group of all the members and add any events to meet with them.
If you don't need to rehearse, Groups has a great place to add any resource people might need.