Both can be recharged.
Zeolite will absorb(?) ammonia, which is a very helpful feature in an immature tank. Rather than recharge, I leave mine in as filter media once it is exhausted. Removing it for recharge could result in the removal of a fair proportion of your filter bacteria. People sometimes talk about how Zeolite shouldn`t be used as it starves the bacteria colony. Their argument is the rise in ammonia levels when the Zeolite is removed, but I believe this is just the result of removing a percentage of the bacteria colony that has inhabited the Zeolite. With all that ammonia stored in the Zeolite, why wouldn`t nitrifying bacteria want to move in? It is great stuff because it takes ammonia out of the water column, making it unavailable to algae.
Purigen is another product I use, but it is different to Zeolite. It removes DOC and various organic water discolourants to give gin clear water. When I do a water change, the water I throw away is clearer than the replacement from the tap. I usually have one bag in use, with another one recharged in standby, to reduce the number of times I open up the filter.
Dave.