Despatch vs Dispatch
Despatch and Dispatch are two words very confusing for people as they think they might be using inaccurate spelling. This might come as a relief to such people that both spellings are correct and in fact both words have same meanings. It is just that British English favors the word despatch whereas Americans make use of the word dispatch. According to Oxford dictionary, both spellings are correct and are synonymous for all meanings of the word.
If there is any issue pertaining to the use of i instead of e in the word, it has more to do with difference in American and British English and can be explained by the use of color instead of colour in America. While despatch is a variant of the word that was more popular in the early nineteenth century, in modern writings, dispatch is preferred over despatch. Despatch has more or less disappeared from modern language, though British still insist on using the word despatch as they feel it is correct spelling.
So whether you use the word despatch or dispatch, they both mean the same act of sending and no one can say that you have spelled it incorrectly. No American would ever use the spelling despatch though many Britons have started to make use of dispatch seeing its popularity all over the world.