The genus that includes modern humans is called Homo. "Homo sapiens" are modern humans. Our ancestors had names like "Homo neanderthalensis" and "Homo erectus."
Homo is a Latin word that means man, or human. When it is used as a prefix, as in "homosexual," it comes from the Greek word homos, meaning the same. It is from the word "homosexual" that the noun homo is shortened and takes its second meaning — a derogatory term for a homosexual or gay man. Its use is offensive, and you should use other terms instead. It is spelled with a lowercase h in this use.