What is the story of Lord Hayagreeva, an avatara of Lord Vishnu?

Once two demons named Madhu and Kaitabh stole the Vedas from Brahma. Brahma, saddened by the theft of the Vedas, sought help from Lord Vishnu. Then Lord Vishnu took the Hayagriva avatar and went to Rasatal and killed Madhu-Kaitabh.
According to the second story, once Lord Vishnu smiled after seeing the beautiful form of Goddess Lakshmi. Goddess Lakshmi felt that he was making fun of her, so she cursed Lord Vishnu that his head would be cut off from the body. After this, once tired in the war, Lord Vishnu strung the bow and placed it on the ground and put his head on the tip of the arrow and fell asleep. The gods cut the bowstring to wake Lord Vishnu for the yagya, due to which his head was cut off from the body. After this, the gods got Vishwakarma to attach a horse's head to Lord Vishnu's body. In this way Hayagriva incarnation of Lord Vishnu was created.