It depends on how they plan to remove the stone/stones. You can get a whopping one that can be either extracted or flushed out without surgery. You can get grit or sludge - there is something called a 'bladder flush' which I personally don't have experience of (touch wood). And then there is surgery with general anaesthetic etc. to remove large ones in the bladder itself. I think they can also form in the kidneys and the tubes which run from kidneys to bladder but that is a more specialist topic and the chances of successful surgery go down. Bladder/urethral stones are unfortunately quite common but there are measures to take to reduce the chances in future, and yes they do occur alongside UTI... it's not an either/or thing.
How old is your girl? Younger ones are able to recover better but older ones still have a good chance with a decent vet. Girls have a bigger urethra than boys and are more able to pass stones on their own. One of my girls was given an opioid injection to kill the pain and then had a large bolus of fluid injected under the skin of the shoulder. It absorbs into the body and makes them pee like crazy. It flushed her out but she was totally stoned and it wasn't nice to see. She recovered quickly once the drug had worn off and it avoided the general anaesthetic so I'd do it again. Another girl had a monster pulled out of her urethra with forceps - again grim, but making surgery unnecessary. If the bladder is blocked it's serious. Be guided by your vet, and good luck x