I know mainly three types of cells in this context and those are referred as open, closed and hybrid cell.
Open Cell : A cell which does not broadcast any "Closed Subscriber Group Id" is considered as open.
Closed Cell: A cell which can be accessed by only closed subscriber group.
Hybrid Cell: A cell which can provide its services to both CSG -subscriber as well as non CSG-subscriber.
If a cell is deployed in a hybrid mode, S1-AP "Initial UE message" sent from eNodeB to MME for an UE carries "Cell Access Mode" IE. Based on the UE subscription stored in HSS, further decisions are taken whether request to be accepted/rejected.
