According to Linguistics there isn't such difference, both are the same language. What makes them differ are some aspects like: vocabulary, pronunciation, spelling and really few grammar rules.
If you think about vocabulary and spelling, there goes a very useful list of synonyms between American and British English - http://www22.brinkster.com/abistene/doubts/AmExBrE.htm
About pronunciation perhaps the biggest difference between British and American English lies in here. In British English, many vowels have different sounds and are usually not nasalized. Stressed vowels are usually longer in American English. In packet, for example, the "a" is longer. #In British English, the "a" in words like can't, class and fast is pronounced at the back of the mouth whereas in America English it's pronounced at the front of the mouth.
#In British English the consonant /r/ is pronounced only before a vowel (for example in red and bedroom). In all other cases the /r/ is silent, sounding more similar to the sound "ah" (for example in car, learn, over). In American English the /r/ is always pronounced wherever it appears in word.
#In American English the "t" between vowels is pronounced as a soft "d" (/d/), so that writer and rider sound similar. British English speakers usually pronounce the "t" as /t/.
#The pot is hot - In British English, the "o" in words like pot and hot is pronounced by rounding lips.
These are just a few of the many differences in pronunciation between British and American English. British English also has a different rhythm, which makes it sounds more "clipped" and emphatic. American English, on the other hand, tends to sound more drawled.
#In American English the "t" between vowels is pronounced as a soft "d" (/d/), so that writer and rider sound similar. British English speakers usually pronounce the "t" as /t/.
#The pot is hot - In British English, the "o" in words like pot and hot is pronounced by rounding lips.
These are just a few of the many differences in pronunciation between British and American English. British English also has a different rhythm, which makes it sounds more "clipped" and emphatic. American English, on the other hand, tends to sound more drawled.
Concerning grammar here are the major differences:
a - Present Perfect x Simple Past - In American English (AmE) the Simple Past can be used with already, just and yet. In British English (BrE), the Present Perfect is used with these adverbs. AmE: I already gave her the present vs. BrE: I have already given her the present
b - Have x Have got - In BrE it is possible to use have got or have to express the idea of possession. In AmE only have can be used in questions and negative sentences.
BrE: Have you got a computer? Yes, I have vs. Ame: Do you have a computer? Yes, I do
c - Prepositions and particles
Some prepositions and particles are used differently in British and American English:
American English / British English
checking something (out) / check something
different from/than / different from/to
do something over/again / do something again
in a course / on a course
live on X street / live in X street
look around the church / look (a)round the church
Monday through/ to friday / Monday to friday
on a team / in a team
on the weekend / at the weekend
ten after/past four (time) / ten past four
ten to/of/before/till four / ten to four
stay home / stay at home]
Some prepositions and particles are used differently in British and American English:
American English / British English
checking something (out) / check something
different from/than / different from/to
do something over/again / do something again
in a course / on a course
live on X street / live in X street
look around the church / look (a)round the church
Monday through/ to friday / Monday to friday
on a team / in a team
on the weekend / at the weekend
ten after/past four (time) / ten past four
ten to/of/before/till four / ten to four
stay home / stay at home]
d - Form of the Adverb - In informal American English the adverb form ending in -ly is often not used: He looked at me really strangely. (BrE) vs. He looked at me really strange. (AmE)
e - Irregular Verbs - In British English the past simple and past participle of many verbs can be formed with -ed or -t, for example, burned/burnt. In American English only the forms ending in -ed are used:
They burned/burnt the documents. (BrE) vs. They burned the documents. (NAmE)
When the past participle is used as an adjective, British English prefer the -t form, whereas in American English the -ed form is preferred, (with the exception of burnt):
a spoilt child (BrE) vs. a spoiled child (NAmE) burnt toast (BrE and NAmE)
f - Go x Come and...
In these expressions "and" is often omitted:
Go and take a look outside. (BrE) vs. Go take a look outside. (NAmE)
They burned/burnt the documents. (BrE) vs. They burned the documents. (NAmE)
When the past participle is used as an adjective, British English prefer the -t form, whereas in American English the -ed form is preferred, (with the exception of burnt):
a spoilt child (BrE) vs. a spoiled child (NAmE) burnt toast (BrE and NAmE)
f - Go x Come and...
In these expressions "and" is often omitted:
Go and take a look outside. (BrE) vs. Go take a look outside. (NAmE)
g - On the telephone
Hello, is that David? (BrE) vs. Hello, is this David (NAmE)
Hello, is that David? (BrE) vs. Hello, is this David (NAmE)
That's it fellas!!! Next time you get worried about having American or British English, just keep in mind to use the language properly, regardless it's American or British.
"England and America are two countries separated by a common language." (George Bernard Shaw, Irish writer - 1856-1950)