You need a specific cover letter, or your resume may not get looked at. You only have a few seconds to impress a hiring manager enough to select you for an interview. I know hiring managers who screen every application personally, and they tell me that if you don’t show what you can do for the company in the first paragraph of your cover letter, you’re not going to get an interview.
You should also target your resume to the job. It’s not just your cover letter. Your resume should be edited and tweaked, so it’s as close a match to the job as possible. Otherwise, it may not get picked up by the applicant tracking systems companies use to screen resumes or the recruiter who reviews it.