Let’s settle this, once and for all.
CV: An in-depth document with a big level of detail about your achievements, more than a career biography - covers education, awards, publications, presentations, trainings, etc. This should be a more formal, static document and you add to it as your career develops.
Resume: Shorter document that doesn't have to cover your whole career and should be customized for applying to a position. The intended reader shouldn't dwell on this for too long - they should be able to scan and get an immediate understanding of who you are, what you know, and what you've done. 1-3 pages max.
Translation? A CV is an all-encompassing document of your entire career. Your resume sends a one-two punch to show your most relevant accomplishments and skills, tailored for a certain position.
So when a recruiter asks to see your CV, does that mean CV or resume?
In my experience, this depends on your seniority and experience level. Less than 10 years of experience? Unless you have an extensive publication list or awards or something of that nature (which usually applies if you hold advanced degrees), then a simple resume is the most appropriate.