There are 6 types of wyvern, not including crystal isles wyvern, voidwym or event wyverns. They are fire, ice, lightning, poison, corrupted, and forest. Sadly the last 2 types of wyverns are in tamable, and the other 4 are the rob an egg and run. If you wanted to know, the other 2 types spawn on extinction, with forest being the one in the forest Titan arena, and corrupted being everywhere you can find corrupted creatures.