There’s no such thing as a standard CV or résumé. For anything.
Don’t make the hiring committee do all the work. Organize the information on your CV so that they can easily find what they need to evaluate your suitability for this particular position.
Your aim is to have at least one member of the committee read your material carefully and make a case to the committee that you should be interviewed. The rest of the committee needs to be able to easily find the evidence and be persuaded.
Using standard headings makes a lot of sense. As does having sections that correspond to the ways we typically think about academic work: Teaching, Research, Service. But the order you put those things in, and the level of detail you provide should be tailored to the specific job for which you are applying
If you are applying for a job that says a lot about research expectations in the job ad and is in a university that defines itself by its research excellence, you want the heading for the research section to be on the first page of your CV. The teaching section will come after this research information.
However, if you are applying for a job in a teaching stream or at an institution that clearly prioritizes teaching, then that section should come before Research.
If you are applying for a job that specifically requires experience of knowledge mobilization or the ability to work in partnership with non-academic organizations or communicate to non-academic audiences, then create a separate section for this and locate it according to the priority it has in the job ad. In most universities it is unlikely that this is more important than traditional scholarly research so put that first, but make sure there is a clear heading (that resonates with the language used in the job description so the hiring committee knows what they’ll find here).
What goes in each section
The most important part of that research section is your publications. Academic publications, publications based on your research for non-academic audiences, and conference presentations should all be listed in separate sub-sections.
In the teaching section, you should list teaching experience as you would work experience in other kinds of jobs: the title you had, the department and university, the dates. There should be enough detail to enable the hiring committee to determine whether you have been responsible for various sub-activities: giving lectures, conducting small group classes, grading, course design, designing assessment, etc.
You should also indicate specific courses you have taught that are relevant to the position for which you are applying. They don’t just want to know what specialist courses you will teach. If there is evidence that you can teach core courses, make sure it is obvious.
Use your judgement
In the early stages of a hiring process people are going to skim your CV. Make sure that the organization of your CV reflects the priorities of the hiring committee and makes it easy for them to find the information they need to make their decisions.