If you don't want to confuse hiring managers and risk them passing on you for a job because you look like a liar, then be sure to make the Work History sections on your resume and LinkedIn profile identical.
Most recruiters will first skim your resume to see if you are a basic match for their open positions. Things like job titles and accomplishments are reviewed quickly for key pieces of info. If they like what they see, they then forward by email your LinkedIn profile and resume to the hiring manager. Now, if the hiring manager opens both up and sees the Work Histories aren't identical, they will start to question which one is accurate.
For example, a true story...
A job seeker I know (before he was a client of mine), customized his resume for a job he wanted. He replaced his job titles with names similar to the one listed on the job posting and adjusted the bullet points to highlight his experience in a way that made him look like a match for the job. This got him through the online application process. The recruiter forwarded him on to the hiring manager. Next, the hiring manager reviewed the resume and then clicked on the link to the job seeker's LinkedIn profile. The hiring manager wanted to see if they had any connections in common. However, when he skimmed the job seeker's profile, he saw the job titles and accomplishments online didn't match what was in the resume. Suddenly, the job seeker was seen as 'gaming the system' and the hiring manager couldn't tell which one was right. The result? The candidate was tossed from the process. How does he know? The recruiter, angry for looking like he didn't do his job right to the hiring manager, emailed and told him what happened!
To tailor your resume for a specific job, focus on the top-fold
You can still adjust your resume to better match a certain position by creating a top-fold that highlights the skills and expertise needed for the job. The top-fold is the first thing a person sees when they open your resume. Two simple columns of your strongest eight or ten transferable skills that match the job you are applying to will help the recruiter and hiring manager get a sense of your strengths. Then, on the lower half of the resume, keep the Work History job titles and bullet points the same as the LinkedIn profile for consistency.