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.
And, BTW, to show the actual seriousness with which ILM views all this stuff, read this quote from an ILM model maker from ST IV:
"We had an incident in the beginning of the film, where we needed a Reliant-class [sic.], so we put a new paint job on the old Reliant model, changed a small shuttle called the Grissom to the Copernicus and we added a back half to the shuttlecraft that Scotty flew around in Star Trek The Motion Picture."
So a member of ILM's model building staff in charge of renaming and re-regging the models thinks that the Grissom was a small shuttlecraft.