What are differences between the word ancestry in English and American English?

American English and British English

American English is more open to creative change and has received a greater influence from other languages. British English is more set in its ways and changes more slowly.

An interesting example to illustrate very basic differences is Automotive Parts terminology. The American invention of the car added countless names for the many auto parts. Rather than using American terminology, British manufacturers chose to create their own and distinctly different names for those many new inclusions in English vocabulary.

To actually answer the question as it has been asked:

The ancestry of words in both languages remains essentially the same. Naturally, because of the other cultures occupying the lands near the UK and the USA, language from these cultures has made its way into the common English language. Words derived from the Native Americans of North America are commonplace in American English, while in UK English can, of course, be seen the influence of Scottish, Welsh and Gaelic words. It is interesting to note that both the English and the Americans pronounced their words with a distinct rhotic accent: yet this has largely fallen into disuse in British English.

American English has its basis in UK language, and thus some words in both types of English are derived from Latin, Greek, French, Italian, etc. words. As new cultural groups from Europe and the Americas settled in the USA, they brought their own influences as well.

While the ancestry is largely the same, the development of these words through the centuries has diverted. UK English has retained its original form as much as possible, whereas the early American colonies attempted to shrug off English cultural ties, and spelling was one way in which they sought to show their independence. Thus, the 'u' was dropped out of words such as neighbour, favourite, rumour, etc; letters were dropped off the ends of words such as dialogue, catalogue, etc.; and changed the s to a z in words such as capitalise. These are just a few examples.