I have been told that the different American spellings of written English words is a throwback to older versions of the language. With regard the spoken language, some American accents probably do have close links to older English, but so do some English accents - these are the two often stated to be the most closely related (and one I am very familiar with) :
Neither sound that similar to Southern American to me, but linguists can probably hear some commonality.
I thought Ulster Scots was generally reckoned to be the closest as a lot of them settled in what were to become the southern states.
I thought that American English spelling was largely down to Noah Webster, although he might well have revived older variants.