While each company will have it's own definition of the cover offered within each type of vehicle recovery membership, generally, the following will apply:
"Single" covers you as the driver or passenger in any vehicle.
"Joint" will cover you and another person, living at the same address.
"Family" offers cover for you and your family. However the definition of family cover can vary from provider to provider. Some major breakdown companies cover you and up to four named members of your household, while other family policies might cover two adults and two children under 21 who all live at the same address.
Personal or vehicle-based cover?
Some of the major providers offer the option of insuring the car or the driver. For example, when buying breakdown cover, look out for the term "personal cover" - this will provide car roadside recovery rescue cover for the insured no matter what car they are in and whether they are driving it or not. You are the member and not the vehicle.
Vehicle-based Membership covers the named vehicle regardless of who is driving and normally costs less than personal membership.