Both countries have a wide range of regional dialects that are very distinctive. And both countries now have different migrant groups. The UK has a lot of African, Indian and Pakistani migrants from their now defunct Empire. The US has a lot of Spanish, continental European and African influences from migration, the slave trade and wars with the Spanish in America.
So if you put that all together, there are many differences in the language composition between the two areas. Each has words that occur commonly only in their area. The most likely thing that you would encounter in writing is a spelling difference, US English tends to use "s" rather than "z" and words like colour and centre are spelled differently.
Native English speakers can generally recognize where someone comes from and understand the speech patterns. If you want a much wider appreciation of the differences, the BBC produced a series of documentaries called "The Story of English". I do admit some of the really small and isolated English sub-dialects needed to be subtitled.