Single payer- Government pays for healthcare, rather than private insurers, like in Canada. Healthcare is guaranteed as a right.
British style NHS- Healthcare is treated as a right, but private companies can operate through the public system.
Public Option- Healthcare is a right, but a private healthcare industry also exists, separate from the public system.
Affordable Care Act- What we have now, with the individual mandate and whatnot
Medisave (Singapore)- Healthcare is not free, but costs are reduced, and compulsory saving accounts allow citizens to save money for healthcare.
Private system- Little to no government intervention in healthcare.
I personally prefer public option style healthcare myself, although NHS and single payer would be preferable to other systems.