Why is there a difference in spelling of certain words in the USA and England?

Most of the spelling differences are the result of Noah Webster's dictionary in the very early 19th century. He actually proposed a rather sweeping spelling reform, but only a few modest changes caught on in the United States: honor from honour, theater from theatre, etc.

Because either way you spell it the pronunciation is the same.

Ex: grey, gray

Remember language changes as new cultures and studies are interpreted into it. American English is almost a completely different language from British English.

This is a simple matter of linguistics. An isolated community develops a dialect indigenous to that area. eventually those dialects become separate languages, just as GB has Irish, Welsh, Scottish (etc) languages.

If it weren't for mass communication and transportation we would have thousands of languages in the US.

Because English is such a complicated language - Americans have 'simplified' it by dropping, mainly, the 'u' from words.

They've made it more phonetic.

Yeah there's colour and color, favorite and favourite, grey and gray stuff like that. But mum is prounounced and spelled differently.

Or "potato" and "potatoe" by Clinton?