The two sites are different companies, both owned by the Amazon group. They have different books partly because books published in one country are sometimes not licensed for another. This is an especially big problem for English-language books moving between the USA and the UK, but the same issue pops up with French-language books between France and Quebec and Spanish books between Spain and Central and South America.
In general you will find a greater selection on Amazon.com, the American site, simply because its market base is a whole continent. The prices are lower as well. In principle you can buy from Amazon.com, but shipping to the UK can be expensive and in the Amazon Marketplace there will be sellers who don't ship abroad because they aren't set up to deal with the customs complications.
Nobody living can ever stop me
As I go walking my freedom highway.
Nobody living can make me turn back:
This land was made for you and me. (Woody Guthrie)