In spite of and despite mean the same thing:
in spite of: without being affected by the particular factor mentioned (1); used to say that something happens or is true even though there is something that might prevent it from happening or being true (2)
Example: He was suddenly cold in spite of the sun.
despite: without being affected by; in spite of
Example: He remains a great leader despite age and infirmity.
The two terms are interchangeable: I love him in spite of his flaws. I love him despite his flaws.
Note that despite does not use of. The phrase in despite of is archaic and no longer used. (1) Note also that the phrase in spite of uses three words–not inspite of.
(1) New Oxford American Dictionary
Photo credit: Mountainair Arts