From most exclusive to least and from highest quality to least: Alligator skin (exclusive), Deerskin (can be wet), Goatskin (delicate, prone to "peeling" ), Lambskin (soft, lightweight, prone to stretching), Calfskin (the firmest, has a balance of softness vs durability) and Pigskin.
Shearling is softer to the touch and lighter in weight than Sheepskin.