Extraterrestrial intelligent beings are not members of alien races, they are members of alien species:
There is some variation in the the appearance of Vulcans: Blonde Vulcans in Star Trek?
And the answer to Is Tuvok the only black Vulcan? points out that the human actors who portray Vulcans are usually "white" but include some "black" humans as well. I think that Asian actors have sometimes portrayed Vulcans also. Thus there is considerable variation in the appearance of Vulcans due to considerable variation in the appearance of human actors portraying Vulcans.
As for Klingons, it sometimes seems like every new movie or television series gives the Klingons a slightly different average appearance. When Star trek: the Motion Picture appeared in 1979, many fans complained that the Klingons in it were so different that they weren't really Klingons at all.
In TNG and later productions, many, but not all, Klingons have been portrayed by "black" actors, while in TOS and TOS films most Klingons were portrayed by "white" actors. Thus there is considerable variation in the facial structure of Klingons, at least in the parts of the actors' faces that show beneath varying amounts of makeup.
In TOS the very human looking Klingons were portrayed by "white" actors with varying amounts of dark makeup, and so the apparent skin color of TOS Klingons varied a lot. Furthermore, in the first Klingon episode "Errand of Mercy" Klingons had eyebrows which split at the sides, while TOS Klingons had non split eyebrows in some later episodes.
And then there is Star trek: Discovery in which Klingons look a lot different from other Klingons. In fact I think that a number of fans complain that they aren't really Klingons because they look so different.
When Dax, a Trill, was a regular in DS9 the fans noticed, and many complained, about how different the Trill were compared to the Trill in the TNG episode "the Host". So it is certainly possible that both Trill hosts and Trill symbionts have different races or even different species.
I think that I remember that in one of Phil Farrand Nitpicker's books he commented on how different some members of some species appeared compared to other members of those species.
The site Ex Astris Scientia has a section called "investigations" about various inconsistencies and problems in Star Trek. That includes discussions of the changes in the appearances of various species in Star Trek.
And of course one possible explanation of why different members of the same species look different is that they might be members of different "races" or subspecies of the same species.