Sometimes, these two are recognized as two separate Gods and sometimes they are one and the same.
Area of Power:
God of Thunder
Myths as Ilyap'a
Ilyap'a is brother to the Milky Way. When he fires a sling at a water pot carried by the Milky Way, the cracking of crockery is what produces thunder and deluges. It is also said that he keeps the Milky Way in a jug and uses is to create rain.
In times of dire drought, simply tie up a black dog until it's wilting with thirst. Ilyapa will take pity on the poor creature and send rain in abundance.
He appeared as a man in shining clothes, carrying a club and stones. He was formerly the main god of the Kingdom of Colla after which the Qullasuyu province of the Inca Empire was named.
Myths as Apu-Illapu
As Apu-Illapu, he is thought to of worked hand-in-hand with Apocatequil, the God of Lightning.