Hi,
I would use two custom forms for that and control the sharing settings for each form corresponding to the team.
Working with sections within a single form will not work out, as you will not be able to control edit rights on team basis.
Depending on the possibilities you have (e.g. Fusion), you need to define the workflow, like which team starts and how the issue is passed to the other team.
To define the start team, you could work with Routing rules. To inform the second team, that they have to do something, they need to be manually assigned or e.g. triggered by a custom status the assignment is done automatically via Fusion.
Regards
Lars