Join the club! I'll tell you how we're using both on our brand based on our understanding.
We use Ticket Teams to automatically assign tickets based geographies, as an example. This allows the user to come in and say I want to see all my tickets, and it'll show them all tickets where they're a member of a Team. Ticket Team members are managed through either Manage Teams within ticketing or Roles within Dashboard roles. Yes, yet another confusion point - when you go into Manage Teams, it shows dashboard roles on the list.
We then use Ticket Groups to give users at the leadership level the ability to filter tickets based on geographies. If they filter to My Tickets, they won't see anything since the groups are not consisdered such. Groups are managed through the Manage Permissions, and it's super manual since there is no way to either bulk upload or download lists.
Good luck!

InessaG Thank you for helping me try to understand this. Based on what you wrote, the key difference is whether or not I want the users to automatically be assigned as an owner or not. If I want them to own it and be notified, then use Teams, if just want them to have access then I use Groups. Correct?
If I have a ticket as part of a team and a group, can members of the group (who aren't on the team) still pick up tickets from the Queue or because the tickets would already be owned by the team would Queues be incompatible?

jmborzick I haven't used queues, so can't really help you there.
FYI, I use both Teams and actual individual ownership assignements. In some cases, I have the account owner assigned as the owner, and in some cases it's a team of employees who own follow-up.

You can upload a file of users into Ticket Groups https://www.qualtrics.com/support/survey-platform/actions-module/ticketing/ticket-permissions/#CreatingFile