Update 2017-01-08: Fixed a few links.
Update: 2015-09-25: Fixed a few links.
The UK & Europe
In the UK, Europe and other parts of the world, you send a CV (or curriculum vitae) when you apply for a job.
In the US and some other places, you send a resume (or résumé or resumé) when you apply for most jobs.
In the US and some other places, you send a CV (or curriculum vitae or sometimes vita) when you apply for a job in fields like science and education.
Difference between CV & resume
So what's the difference between a CV and a resume?
Well for many people, there isn't one. When many people in the UK (and elsewhere) say "CV" and in the US (and elsewhere) say "resume", they use those words to mean the same thing: a short document (1-2 pages) about themselves with important information like work experience and education, which they send to an employer when applying for a job.
However some people say there should be a difference between the two.
They say a CV :
Whereas a resume:
If keeping the CV the same for all job applications, then what changes is what you write in the cover letter. You adjust that depending on the job and employer.
Science & Education
When applying for jobs in fields like science and education (in both the UK and the US, as well as elsewhere), you send a CV (not a resume) and it'll be longer (2-5 pages) and more detailed. For example it might include names of all the articles you've published, studies [#5] or research you've been involved in, or professional associations you're a member of.
So here's a summary:
UK, Europe & some other countries:
US & some other countries:
Not sure which? Check.
If you're not sure which word or format/length to use, check with the employer's HR department or website and find out which they prefer. You could even try asking (by phone or e-mail): that would help you get it right and show you're serious and professional about this job application and start building a relationship with their HR department, so that you're more than just a name on a piece of paper.
They might even offer a template [#2] (e.g. a Microsoft Word file) you can use to make your CV or resume.
Here are some links with more on this topic of CVs and resumes:
You have probably noticed the different ways of writing "resume / résumé / resumé". I've written another post about that, as well as about its pronunciation.
G.A.L.E.S.L. / joe3
Some tips and links on learning English.