The overall body/type standards are very, very similar. A couple coat colors are slightly different. For example, in one (but only one) US club, pink-eyed black is called lilac. In the UK and the rest of the US, it's called dove. There are standards for colors in the US (splashed, American brindle) that don't exist in the UK.
A mouse I bred in the US could be shown in England and a mouse somebody in England bred could be shown over here.
Of all English-speaking countries (historically the primary locations of the mouse fancy), I think the standards of the UK and US are probably the most similar overall.