This happens when people applied to two programs and were ineligible for one, but eligible for the other. There are two main unemployment benefits programs you can apply to: regular unemployment insurance (UI), and the Pandemic Unemployment Assistance (PUA) program. You can’t be eligible for both at the same time.
So if you got one denial letter and one approval letter, the letters are about two different programs. You will be getting benefits for the program you got approved for. Be sure to file your weekly claims to get your benefits each week.