A group is made when a number of participants register together under one booking (this can be broken into multiple payments). Registering as a group helps to speed up the booking process for large parties, and can help to accrue group discounts.
A team is a collection of participants who wish to compete as a team, and receive a team score/ranking.
The key difference between a group and a team is that a team functions for scoring and results, whilst a group functions for group bookings and availing of discounts.
You can be part of someone's group booking, but not necessarily part of their Team. These two things are separate from each other.