Why there are differences in words/usage between British English and American English? which one to follow for correct English?

Language is not static: it goes on changing. The English we learn today is entirely different from what it was in Chaucer's time. English people who landed in Americas centuries ago also couldn't stop the phenomenon. This is one plausible answer to 'Why?'

Both British and American Englishes are correct in their own rights. There are no syntactical differences, only minor morphological differences. We cannot say that only American word spellings are correct, or the other way round. The same is the case with pronunciation. Both are correct; in fact, even in America and Britain different regions have different pronunciations. Since, computers and the leading softwares are from America, we feel American English is correct because the autocorrect feature displays American spellings. If you set this feature at British English, most of the words it shows wrong will automatically be shown right.    

American English would most likely be correct if any discrepancies arise. Words that have the same past tense and present tense are widespread in British English such as fit (with fit also being its past tense whereas fitted would be the past tense in American English). American English also expresses collective nouns correctly considering it as a single unit and therefore considering it a singular noun rather than a plural noun which is acceptable in British English but sounds quite wrong.

Thanks for the invite, I apologize for the answer, I do not know, I leave the answer for the professionals .

i think British is standard and first reference

1- Linguistic variation happens geographically within Britain. Therefore, it is not strange to notice differences. Languages change naturally. It is inevitable.

2- British English is no longer the standard English as widely believed. Today, we have standard British, standard American and standard Australian.

3- There is a kind of intelligibility between different Englishes. If you stick to one, or even mix many, it is the same. You are still understood.

4- Sticking to one variety, on the other hand, makes you belong to the speaking group and makes you sound like them. It is up to you.

It is somewhat like dialects in the Arabic language. Both are correct and you can follow whichever easier for you. But if you are studying in Britin or America then you have to follow the style and words usage of that country.