The two certain wild cat species in Utah are (1) the bobcat and (2) the mountain lion (aka puma). The third possible wild cat species in Utah is the Canada lynx. The reason why I say there is some doubt about the Canada lynx is because Wikipedia indicates to me that this species of wild cat is present in Utah but the definitive answer should come from the IUCN Red List of Threatened Species (Red List) and they are clear in stating that it is not quite present.
I suspect that Wikipedia is out of date. The books that I have are certainly out of date because the distribution of the wild cats is ever changing – shrinking in fact.
The Red List informs us that the Canada lynx has been reintroduced into a neighboring state of Utah, Colorado. However, the map clearly indicates that the reintroduction of this medium-sized wild cat species does not extend into Utah (see cropped version of map aove). I would say with certainty that there are two wild cat species in Utah namely, as mentioned, the puma and the American bobcat while the third is a poor possibility; the Canada lynx. I hope this helps.
There are many other pages on this website in which I discuss the presence of wild cat species in the various states of the USA. Please use the search facility in the right-hand column to find these pages. If you search for “wild cat species in” Google will find them.