They are supposed to be seperate classes, the primary difference being the K't'inga has an aft torpedo launcher and the D-7 does not. There's also differences in size and surface details. Presumably the D-7 is an older ship to account for why there's none of them in the 24th century but still plenty of K't'ingas, even during the Dominion War.
Apparentally, even the shows have got this mixed up. The Klingon ship iin Voyager's Prophecy was stated to be a D-7 in dialogue even though it is clearly a K't'inga. Likewise, one would think they meant to use a D-7 in Enterprise's Unexpected, even though they used a K't'inga. Presumably this is because a CG mesh of the K't'inga exists and since that's practically identical to the D-7 they figured who the hell would care? In fact, Unexpected was supposed to be a new Klingon design, but they didn't have time to make a new CG mesh so they just used the K't'inga since it had a retro look to it.