Every Planner plan uses Office 365 Groups to keep track of its members. So every plan needs a Group to exist. You can, however, create multiple plans using the same underlying Group.
Because Teams are also built on Office 365 Groups, you can only add a plan to a Team needs if it uses the same underlying Group.
You can't copy plans from one Group to another. You can only create a copy of a plan within the same Group.
You can't copy or move tasks to another Group. You can copy and move tasks within the same plan or to another plan within the same Group.
For more details, see Learn about Office 365 groups.