What's the diffrence between hammer toes, bunions and corns?

All different. Hammertoes are the contracture of the lesser digits. Bunions as the lay person describes them is the deformity of the great toe as it begins to turn toward the second toe, sometimes crossing over/under it and the large bump on the outside of the big toe joint. A corn is a callus on the top of the foot and are commonly seen on hammertoes.
Different entities. A hammertoe is an abnormal increased contracture or a bending of the toe joint. A bunion is a progressive disorder that is often described as a bump on the side of the big toe joint which may become painful. Corns are hardened patches of skin that commonly occur at bony prominences due to excess friction.
Callus vs. bent toe. A toe that has drawn back and no longer sits straight or "flat" is a hammertoe--this is usually in reference to one of the smaller toes, not the big one. Corns are the calluses that often develop because of the underlying hammertoe deformity. A bunion is the bump that forms at the big toe joint, associated with the toe leaning toward the lesser toes.
Several things. Hammertoes are deformities of the smaller joints of the toes. Bunions can occur at the big toe or small toe where the metatarsal bone is pushed out of position towards the adjacent toe and the metatarsal bone is prominent. Corns are thickening of the skin due to irritation.