Basically yes. But more specifically, graduate students in American universities will have had 2+ years of courses and have performed 4+ years of research. My understanding is that PhD students in the UK just finish at the end of the third year. In the US, you are basically done, when your project is completed.
You're on the right lines, but it's not time itself that's important ;)
I'm a British student taking my PhD in the US. The core difference is publication record: in the UK, publications while doing your PhD are simply nice to have. In the US, they are essential. This is one of the key time-stretchers (alongside having to take classes and being able to change your thesis at any time).
This roughly means that a PhD that has just graduated in the US is immediately hirable all over the world, whereas a European will not be able to take a job in the US until they've spent time building a publication portfolio after graduation.