Condo = unit owners own fractional interests in the shared areas (including the building and land).

Co-op = the cooperative owns the shared areas; the members own shares in the coooperative entity.

Both = the entity (HOA/cooperative) pays for the maintenance/other costs of the shared areas. Co-ops collect the money for these expenses through monthly dues and yearly assessments. I do not know how co-ops collect for these expenses.

My unit is a condo; I fractionally own portions of the building and land. My condo pays for the expenses associated with the common areas through monthly dues and yearly assessments.