[Arnabas]

Like I said before, though, the Klingons in the original series (with Kirk, Spock, et al.) DO look the same as they ones in the movies, Next Generation, etc. We just can't "see" it. This was Roddenberry's own explanation. We have to imagine them the way we know them now because they didn't have the budget/ skill to make them look that way in the '60s. So no discrepancy there.
If you don't like that, then accept the alternate answer from "The Final Reflection" which says that the early Klingons were genetically altered to appear the same as whatever race they were dealing with. I.E those that dealt with humans looked more-or-less human and those that dealt with the Romulans had Romulan features.