Despite and in spite of mean the same thing. They are prepositions used before nouns to introduce a contrasting fact. For example, "Despite the heat, she would not take her coat off" or "In spite of the heat, she would not take her coat off". In spite is always followed by 'of' and do not use 'of' after despite. Both despite and in spite of can be used to introduce a sharp contrast between two facts, such as "In spite of all their money, they are still not happy".