Daedalus
The Daedalus-class was commonly used design in the early days of Starfleet in the mid-22nd century.  Unlike most later starships, the Daedalus had a spherical main hull.  The last ships of this class were taken out of service by the year 2196.

A Daedalus-class model labeled as USS Horizon can be seen in Sisko's ready room.  It is based on an early design for the original USS ENterprise by Matt Jefferies which is depicted in The Art of Star Trek.  Although we have never seen a close-up that would allow us to identify it as Horizon, I think the design is 100% canon.

Since the Daedalus-class was retired before 2196, it is unlikely that the USS Carolina (TOS: "Friday's Child") belongs to this class, although this is stated in the Star Trek Encyclopedia II.  Since the ship was only a Klingon hoax anyway, we need not bother about theories to explain why this particular Daedalus-class was still in service.  But it may be possible that they took the name and registry from an old databank, and that it is a long retired Daedalus-class ship.