* CVs are generally longer - 2-4 sides. Resumes are more of a one page and done thing.
* Resumes often include a mission statement or similar. CVs don't - you'd put that stuff on a 'cover letter', if at all
* CVs are generally not adjusted per job - it's everything, with only the older stuff abbreviated. Whereas resumes are tailored.
In the UK I created CVs, in the US I created Resumes.
Same thing, different names.
However, as an American, I've never heard of a résumé including a mission statement or being adjusted per job. As you said, they're very short documents. I've always seen them just giving the same factual history of the person's employment/education, and the person similarly attaches a cover letter tailored to the specific job, repeating some highlights and how it qualifies him and saying how perfect this job is for him.
[1] Sidebar: Every bit of résumé advice is "fighting words", with diehard adherents on opposing sides. In this instance, "1 page" can be taken as "What have they been doing with their life? Discard it.", while "2 page" can be taken as "Wasting my time. Discard it.". The most successful strategy is hard to achieve: know the personal pet-peeves of the recipient, and adjust accordingly.