Q. Can your LinkedIn profile and your resume be different?
A. Absolutely. While the two need to be complimentary and have consistent “branding,” they each serve a unique purpose.
Your resume is a more agile marketing document, which means it can (and should) be tailored toward each specific position that you apply to. This also means that you may choose to exclude unrelated experience / skills or reframe your experience so that you are highlighting specific attributes.
While your LinkedIn Profile is flexible, it is more static than a resume; you are not going to be targeting it toward specific opportunities. I recommend that clients use LinkedIn to provide a high-level overview of their professional experience and skills. So I suggest that LinkedIn be an entry-point for interested parties, with a resume being a "next step" document that provides more details about areas of your experience and accomplishments.
As I mentioned above, no matter which approach you take, it is important that your resume and your “social” resume be on-brand and consistent. Think about all of the elements of your job search as a comprehensive personal marketing strategy.