I don’t know too much about the British side of things, and a lot of it sounds similar, but one difference I know is that CVs can be multiple pages and are a little broader. In my experience, mostly artists use CVs in The States. I have one as an artist, and I find the fact that I can use more than one page really liberating.
Resumes, which is what we use, almost always stick to one page, so you really have to be brief and careful about what you choose to include. We, like the Brits, are definitely are trying to sell ourselves with both the resume and cover letter, but I personally always stay away from exaggerating. And then, most friends of mine loathe writing cover letters because you have to make yourself sound so hireable, but you don’t want to sound full of yourself at the same time. So, you have to sound SUPER confident without sounding like you’re bragging. It can be such a hard style.