But do they have different stats?
None of those pictured have stats associated with them, as far as I know.
Those are just examples of the various designs for axe heads and handles.
When you find an axe in a chest, or possibly recieve them from a quest, they'll randomly have one of those heads and one of those bodies.
The stats of those weapons will also be randomised, depending on the level of the quest, or the world they're found on, or the biome they're in, as well as any special effects they may have.