"Z" is a designation which means a steel shield covering the one side of the bearing (for most brands). "ZZ" means that the bearing has a shield on both sides.
Normally, the shield itself will be branded as "608 Z" even though there is a shield on both sides of the bearing. This is for practicality in manufacturing. It is much more economical to produce all the shields stamped as "608 Z" than it would be to manufacture the exact same component with two different stampings on them.