I have both a resume and a CV; I am a research scientist with a PhD and two Master's degrees.
Both a resume and a CV are telling a prospective employer what you can do for them, and how you can be a part of their team. But they are used to apply to different kinds of jobs.
My resume is used to get technical contracts applying my skills to solve somebody's problems, to develop their products or somehow to satisfy their clients (or the law). In order to convince them I am right for the job, I focus on the skills they need: The technical and engineering tools I am proficient in using, my skills in management or various protocols, whatever is applicable to doing the work they need done. I include previous successes in this kind of work, and the types of problems I have successfully solved for other clients.
I do list, on the resume, my credentials and awards or other professional recognition; but at the end; and that I have published X peer-reviewed academic papers, available on request.
A CV is applying for a different kind of job; one more academically oriented (like my current job, research scientist). It is still oriented toward what the employer wants to see, but that is different. The job of research scientist is roughly "Inventor." I collaborate with others to invent solutions to problems nobody in the world has ever solved. It is a creative endeavor.
The same thing is true just for being a college professor (I was). In addition to your teaching duties, you are expected to publish original research regularly; to develop new understandings and tools within your field. It is creative.
So academically oriented places of employment want to see what they value: Academic achievement, the degrees I earned. My GPA (4.0 over 12 years of college, all classes). The topics of my Master's theses (both of them) and my PhD dissertation. The scientific Journals I have published in (they are ranked, some are very prestigious; others less so), the scientific Conferences where I presented my work (also ranked).
They want proof I can do the job they need to fill, which requires creativity and originality. That is what a PhD is all about; we are not supposed to hand those out unless the candidate has proven they can make "an original contribution to the field", and we typically judge whether they have done so by reviewing their publications in peer-reviewed journals to see if they actually did invent something new or contribute something new to their field of study. They can't just recycle what is already known and call it new! And even if one school lets a candidate slide on the "original contribution criterion; we ask job candidates to present their research, and if WE think its unoriginal crap, they don't get the job.
So my CV has a LOT of info on the original things I have invented and published about; (well 3 or 4 lines on each) where I published them, how to find the actual papers, how they rank, etc.
Then other things on the CV, like your teaching experience, classes you've taught, or committees you have served on, academic contests you have judged or help organize, things you have done to help a school are all relevant. Schools like a team player.
My advice is, cast your experience and credentials in light of the job the employer needs to get done. That is how you decide what to emphasize (by putting it early) and what to deemphasize. What are the skills they value?
Not everybody wants an inventor figuring out on the fly how to get the job done; most corporations or business-like non-profits want a workhorse that is an expert in existing tools, techniques, protocols and any applicable laws. They want to see your "resume".
But research organizations, colleges with research programs and labs and PhD programs, and some large corporations with applied research departments are looking for inventors and people that can come up with something original. They want to see your CV.
CLARIFICATION added due to comments:
Both resumes and CV's are employer oriented, we are telling the employer what they need to know. But the employers want different things; and roughly those different things are classified as Resume or CV.
An employer looking for an experienced car mechanic wants somebody that already knows everything about how to fix cars. They aren't seeking somebody smart and inventive that can figure out from scratch how cars work so they can teach themselves how to fix cars and reinvent car repair from the dirt up, they aren't looking for a track record that suggests maybe you can do that. They want a resume, showing your experience in repairing different kinds of cars. If they want credentials, it is for training programs in fixing cars. If they want references, it is for people that say you can really fix cars. This is "resume" territory. Similarly if I am looking for a network systems administrator, or car garage manager, or salesman, or applications programmer or most low level engineering jobs. Here's the thing to do, apply the rules you have been taught and get it done.
But there are jobs that have important parts that require innovation, and by "important" I mean that innovation is mostly how you are judged. Most obvious is when your job is to invent new products. A subset of that is inventing new science, which is the job for research scientists and usually for college professors with PhD's. The gold standard requirement for a PhD is contributing extensive and original research to their chosen field. Typically in universities we judge whether it was "original" by whether it gets published in a decent peer-reviewed journal (one that we trust isn't a vanity press).
The "publish or perish" maxim for college professors sums it up. Publish demands innovation that is accepted by the experts in your field (peer reviewers) as a valuable contribution. Perish means innovation is a critical component of your job, we will let you go and find somebody else if you can't invent anything your peers find useful. It's a showstopper, because we are NOT just looking for a good teacher or a helpful colleague. We need an inventor. So here comes a CV, we want to see that you have the education (and grades) that proves you are aware of the state of the art in your field, and we want to see that you have a track record of creating something new with it. That is why we want to see your peer-reviewed publications and your dissertation presentation, it is a way of judging how creative you are and how original in your thinking.
There are many jobs in-between these extremes that may require a blending of the two. Mostly a CV focuses heavily on education credentials and publications, while a resume focuses more on job experience. In-between are jobs that demand an education and perhaps credentials, but not necessarily creativity (like a medical doctor, nurse, attorney, accountant). In such cases we blend the requirements of a resume and a CV, and call it whatever the profession demands. Or we separate them and send both: A resume to describe job experiences, usually in reverse chronology, and a CV that focuses on the details of education and credentials and possible publications.
CV's generally have a fixed format the employer expects to see. It will be as long as it needs to be; although you can cut out early-life work that is not relevant experience. They don't need to know you were a food server or mowed lawns while attending college.
On a Resume; organization is more important than length. Put what your employer likely wants to know most, first, preferably on the first page. Don't be repetitive. Don't include early history that isn't going to matter; I have listed before the age of 24 "previous unrelated jobs available on request." (Except for my two years of military service, out of high school.)
Condense what you have to what is relevant and don't worry about the length. Ignore the advice to stick to 2 pages or three pages or whatever; follow the maxim of Sales: "The more you tell, the more you sell." Just like an advertisement, if what the employer reads on the first page doesn't interest them, they will put your resume/CV aside, no matter how long it is. If everything you put in is relevant without being boringly repetitive, they will finish it, and the fewer "big questions" you leave in their mind, the more likely they are to call you in.
On both, as an employer I'd rather not see any hobbies or irrelevant-to-the-job memberships in organizations, past or present. Just leave out personal interests or qualities or information that were not specifically requested. They may even do you more harm than good.