Your cat would have a blood test which would show FIV in the blood which your vet is warning you can’t tell the difference between vaccinated and active. These guys have Covid in their nasal secretions which means active Covid infection. So the difference between a person having smallpox antibodies in their blood and smallpox lesions on their skin/active outbreak. (Non medical person so I could be way off .)
As I understand the Covid vaccine, there are two different things they want to happen: less likely to get Covid, less likely to get the “hospitalized, ventilator, could die” serious case. The point of the article seems to be “yes, these guys have it, but it is minor” so vaccine did what it’s supposed to do.