Despite and Inspite of

Despite e inspite of são tidos como sinônimos.

Encontrei essa explicação sobre eles no http://www.elearnenglishlanguage.com/

Despite

Despite means "even though," "notwithstanding," or "regardless of." It's the opposite of "because of/due to," and can be used with a noun or gerund.

She had difficulty communicating in French despite all her years of study.

We lost the game, despite the fact that we practiced all week.

Despite not having an umbrella, I walked home in the rain.


In spite of

In spite of means exactly the same thing and is used exactly the same way as "despite."

She had difficulty communicating in French in spite of all her years of study.

We lost the game, in spite of the fact that we practiced all week.

In spite of not having an umbrella, I walked home in the rain