UK vs US

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So, English is very old. Original old English (ex, Beowulf) is not a script the typical English speaker would be able to read: On þyssum geare man halgode þet mynster æt Westmynstre on Cyldamæsse dæg 7 se cyng Eadward forðferde on Twelfts mæsse æfen 7 hine mann bebyrgede on Twelftan mæssedæg innan þære niwa halgodre circean on Westmyntre 7 Harold eorl feng to Englalandes cynerice swa swa se cyng hit him geuðe 7 eac men hine þærto gecuron 7 wæs gebletsod to cynge on Twelftan mæssedæg 7 þa ylcan geare þe he cyng wæs he for ut mid sciphere togeanes Willelme ... 7 þa hwile com Willelm eorl upp æt Hestingan on Sce Michaeles mæssedæg 7 Harold com norðan 7 him wið gefeaht ear þan þe his here com eall 7 þær he feoll 7 his twægen gebroðra Gyrð 7 Leofwine and Willelm þis land geeode 7 com to Westmynstre 7 Ealdred arceb hine to cynge gehalgode 7 menn guldon him gyld 7 gislas sealdon 7 syððan heora land bohtan.

The stuff you read in Shakespeare is Early-modern English.

When Modern English came to the US colonies, the Americans decided to change the vocab and spelling a little bit. Here are some of the differences. Keep in mind that this doesn't even glimpse on culture and region differences.

US - UK

In British English "ou" is typically used, whereas American English simplly uses "o"
color - colour
flavor - flavour
favorite - favourite 

gray - grey

cotton candy - candy floss
flash light - torch
cookies - biscuits
chips - crisps
fries - chips
sneakers - trainers
apartment - flat
elevator - lift
math - maths
fall - autumn
tire - tyre
airplane - aeroplane
draught - draft
ass - arse
bathroom - loo, toilet

inches/feet/yards (imperial system) - centimeters/meters/kilometers (metric system)

fahrenheit - celcius

bloody is used to curse like "bloody hell"

"wanker"

"piss off"

The British equivalent to the middle finger is two fingers with the back of your hand facing out, basically the peace symbol, but your palm is facing you.

I'm certain that this is far from all of it, but here's just a little bit. And the British drive on the left side of the road.

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