The others have some good ideas.
A "uti" is a urinary tract infection - bacterial infection in the bladder and/or urinary tract, causing pain and frequent urination, possibly bloody urine, etc.
"crystals" are just that - crystals that can form in the urine, making the urine very painful to pass - as there are little bits of debris in it. There are different types of crystals that can form, and it has to do with the pH of the urine. Too low pH makes one type, too high pH makes another.
The irritation from crystals can cause a bacterial infection, though. So they can occur at the same time. Either one is very serious in a male cat, as their urethra is very small and somewhat funnel shaped. They can get "blocked" by mucous, crystals, and other "junk"....leaving them unable to void their bladder.
