I would say that Hobgoblins are more Cardassians than Klingons.
They have a super organized society. To be within the top caste of that society, you must exhibit particular behavioral traits. You are to be organized, collected and avoid showing weakness. You are to keep your word, do your duty and diligently accept your chosen role within the clan. You are to avoid doing manual labor unless absolutely necessary and certainly avoid doing anything "unclean"-- there are goblins and other slaves to do such things.
Moreover-- there are plenty of ways to complete differentiate Hobgoblins and Orcs, the only traits they have in common is that they are bigger than humans and a bit beastial and maybe talking about "honor"-- there is more reason to get halflings, gnomes and dwarfs mixed up.
Orcs are highly spiritual, emotional and instinctual.
Hobgoblins are analytical, reserved and intellectual.
Orcs are people with mildly pig-gorilla like features and green/blue skin tones.
Hobgoblins are people with mildly cat-wolf like features and red/orange skin tones.
Orcs prefer to live in dark, damp, cold environments like caves high in the mountains or out on the tundra.
Hobgoblins prefer to live in warm, temperate climates on islands with their own crudely built fortresses or refurbished castle ruins left by someone else.
Orcs are descendants of Giants and kin to Ogres and Dwarfs. Which is why they hate Dwarfs.
Hobgoblins are descendants of Fey and kin to Elves. Which is why they hate Elves.
Orcs will raid your lands and steal your food, generally just killing anyone who stands between them and something they can eat and then they'll go away when there is nothing left to eat.
Hobgoblins will raid your lands and take away anyone they can in chains to serve them-- if not just claim the land for their own expanding empire.
Orcs want to take down the biggest, strongest, nastiest monster there is single-handedly to prove they are the biggest and strongest.
Hobgoblins want to rule the world, eliminate the undesirables and force everyone to live with the efficiency they do.
There are so many fundamental differences here from physical to cultural to psychological, that even when one accounts for the varied personalities of individual members of these races, account for them being potentially every class in the book and even that they may find themselves occupying similar habitats in some regions of the world, there really is very little overlap. They could hardly be more naturally polar opposites.
As for how Hobgoblins relate to other Goblinoids? Well, being that they are a kind of fey, they tend to mutate quite a bit to fit their environment. Look at the endless list of different kinds of Elves who don't even have the advantage of the short-breeding cycles of the goblinoids to account for their evolution.
But the split between Hobgoblins and Goblins is almost certainly one of a strictly controlled caste system where the hobgoblins were the warrior-nobles and the goblins were the serfs. Bugbears probably came about from Goblins who ran off into the woods and slowly evolved to become bigger and bigger to survive the dangers of being in the forests.
But the Hobgoblins are probably the ones responsible not only for evolving themselves away from Goblins, but probably also directly responsible for the Goblins' short lifespans and that they are sneaky and lazy little buggers as all of the serfs who were probably super cooperative just got worked to death meaning only those who were naturally lazy and good at dodging work survived to breed and create the next generation.
But in most D&D worlds, that ancient Hobgoblin empire fell quite some time ago. In Eberron though, it seems it is still ongoing.