Mid-sized Federation Science Vessel. If you really want to pick a nit, it doesn't even call her a Starfleet ship.
The ship was crewed by Starfleet officers, so it makes the Grissom a de facto Starfleet vessel.
I'd say "USS" would identify the vessel as one belonging to Starfleet, not the crew. Genesis had become a delicate matter and I think Starfleet wanted to keep a watchful eye on these enthusiastic scientists, therefore and for this particular mission they assigned Captain Esteban to be in charge of the operation.
Especially since under normal operations I could imagine a commander to be the captain of such a small vessel, but not a veteran Starfleet captain like Esteban.