Yes - always make a cover letter tailored to the position being applied for!
I always used cover letters to talk about the intangibles and things that the resume doesn't convey - just in case the company I am applying to doesn't immediately notice things like 'transferable skills' when I am applying for a job that I may not have held before.
If you have never worked for a pet store before, and you have no real training for that but you owned pets when you were young (or now) and you worked retail and you paid such good attention to something else at another job that you noticed something was awry with x, y or z .. you can say that you have very good attention to detail that would stand you in good stead as a groomer, etc. Not a super good example but I am tired so I apologize - just look for those 'transferable skills' in your job history and use them.
I tell them what it is about my personality that makes me suited for the position I am applying for. I also try to slip in a bit that shows I have researched the position (beyond the basic info that I might have seen in an ad) and the company.
The purpose of a good cover letter I think is to attract attention. Resumes are often boring reading. Tweak their interest in you in some slightly different way than many others would. A good cover letter can make you stand out from the crowd.
Show some personality - but not TOO much unless you are applying to be a clown in a circus maybe. Illustrate your 'drive' in some manner - things that will make you a good employee - but watch out for the standard catch phrases and words. Don't just pedantically say things like 'I am reliable and adaptable' without giving a bit of information that enhances that description.
Be personable but polite, succinct and professional. Get someone else to proofread it and give you tips about content and sentence structure if it seems stiff or too flighty or contains (as I always have to edit out
) too many run-on sentences.