"In spite" is two words. Despite has a number of meanings one of which is the same as "in spite". Despite can mean any of - Disdain, contemptuous feelings, hatred; Action or behaviour displaying such feelings; an outrage, insult; Evil feeling; malice, spite; in spite of Credit - Wiktionary.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.