So the Yelchin is 4774-E and the Gov’Nor is a Cardassian ship, not a Starfleet ship.
According to Memory Alpha's entry, it's both...
Edit: I guess it's possible that the Gav'Nor wasn't Starfleet. Heck, the Kelpiens had their own vessel (the Khi'eth), which was not Starfleet but the Kelpiens were (are?) members of the Federation...
And I admit I'm curious as to what "Nor" means. We've seen it on two different Cardassian ships (the Bok'Nor, from the DS9 Maquis arc, and the Gav'Nor) and also on an entire class of stations (Nor class).