The terms, asura and rakshasa are often used in place of each other. This is not correct. Their origin and genealogy are different.
Kashyapa is the forefather of devas, asuras, manushyas and nagas. Kashyapa's children born of Diti are called daityas. His children born of another wife Danu are danavas. Collectively, daityas and danavas are called asuras. They are half bothers of devas with the same father and different mothers.Some of the famous asuras are Bali, Banasura, Shambarasura, Keshi, Channda, Munda and Mahishasura.
During creation, once Brahma felt very hungry and angry. From his anger originated two rakshasas called Heti and Praheti.They were very cruel and evil minded. They killed and ate lot many brahmins and cows. Heti married Bhaya, the daughter of Kala. A son called Vidyutkesa was born to them. His wife was Salakantaka. They abandoned a child born to them in the Himalayas who received the blessings of Shiva and Parvathy. This child was named Sukesha. He married the daughter of a gandharva called Devavati. They had three sons- Malyavan, Sumali and Mali. Through severe austerities they received the blessings of Brahma and became indefeatable. Thus they became very arrogant and cruel.They made Lanka their capital.
The rakshasas multiplied in thousands. Kaikasi was one of the four daughters of Sumali. She once saw Kubera and understood that his riches and glory were due to the fact that he was the son of Sage Vishravas. Kaikasi approached Visravas and begot four children - Ravana, Vibhishana, Kumbhakarna and Shurpanakha of him. The rest of this is well known.