Sometime yes, sometimes no.
If you are asking yourself “do I need to rewrite my resume for grad school applications?”, you should ask some other questions too.
What is the nature of grad school you are applying to? If it is all research, a CV is appropriate, but a resume is far more appropriate for business and professional school applications. Some schools may require resumes in specific formats, but most will not. After earning admission to an MBA or professional program you may be asked to convert your resume to their standard format, but it is not typical as part of the application process.
One area open for debate is use of an objective statement. I like to see the objective statement say that it is to earn admission to the program I work with, or not be there at all. Resumes with an objective statement focused on gaining a career position sends a signal to the admissions committee that you are not serious and focused on going to grad school at that time. This weakness is easily avoided.
You may want to rewrite your cv if it is entirely focused on research activities and publications if you are applying for a professional school. This will help you direct focus of the admissions committee to the factors that they are looking for and they will spend less time wading through unimportant information.
I advise KGI applicants (typically science backgrounds) that their current resume is all that we want to see. That is the starting point, but after they have enrolled, the resume will be revised to be competitive and formatted properly for our industry (biotechnology, pharmaceuticals, medical devices, bioprocessing operations, and regulatory affairs).