yup, there are standard types. Before the RHIBs came around, the standard types were
1) 26' motor whaleboat MWB (as the picture above, pointed on both ends, sometimes with a fibreglass canopy)
2) 26' personnel boat (enclosed top)
3) for larger ships: 33' Utility Boat UB(open, square stern)
4) much larger ships: 33' Personnel boat
These are all described in the link provided by Mr Stik, above.
A smaller ship would probably have a single 26' MWB. A less-small ship would also have a 26' Personnel boat, which would serve as the Captain's gig. You can tell the gig because it has a red stripe at the waterline, and the name at the bow has an arrow through it.
If a ship has another personnel boat, it would not have a red waterline stripe, but a blue one instead. On Jouett, our second 26' Pers boat was called the Officers' Motor Boat, but I never saw it used specifically as such.
Jouett also had a 33' UB, open with formers to mount a canvas top.
Flagships will have a boat designated as the Admiral's barge, usually a 33' Personnel boat with sides painted black, and green below the waterline. Before the small boats were purged, a CV would have a bunch of 33' boats in the hangar, both open UB and closed personnel boats, with one belonging to the admiral.
For Ticonderoga, we should guess that there is a 26' personnel boat on the stbd side, marked as the Gig.
I hate RHIBs.