The Mission Circle is like a board. It often has external individuals or stakeholder representatives as members. It holds the organization true to its mission and its focus is on the general direction of the organization.
The General Circle is made up of leaders and delegates of department circles (plus in some cases the leader of the GC). They are much more focused on the day-to-day business of the organization, making sure that all the department circles are well-aligned and can be productive.
You can think of the difference as the difference between an advisory board and a management team.
For more information, check out our handbook Many Voices One Song section 2.5