In trying to come up with a satisfying answer to pony genetics, I stumbled upon this idea that the different types of ponies may actually be hybrids of distinct species rather than races of the same species. This would better explain why some traits are common to all types while others are unique, as well as the very occasional cross breed like a pegacorn. This also adds some explanation as to the ponies' ability to cross breed with just about every other species, at least according to the fanon.

Essentially, the species of ponies are all of the Equus genus, which also includes zebra (a common cross breeding option), and Thestral.

This post will discuss the three mentioned in the Pre-Equestria post, with a brief mention to crystal ponies, with other species and hybrids being discussed in later posts depending on interest.

Unicorns

The unicorn species is a bit taller than unicorns depicted in the show, not quite alicorn height, and a fair bit more slender. In terms of build, Fleur De Lis is an excellent example. Unicorns also tended to have longer, but more fragile, horns, and were capable of great feats of magic that now only alicorns can replicate, hence why they had no issues with the sun, moon, and stars, before the alicorns arrived. The final distinction between the species is the tail. A unicorn's tail was much more similar to our traditional depictions, appearing like a lion's tail with a long slender prehensile portion ended with a tuft of hair.

Pegasi

The pegsus species is a bit more birdlike than depicted in the show. While their build is mostly unchanged, ancient pegasi did not need magic to fly, having hollow bones to reduce weight and significantly larger wings, about twice the wingspan as a modern pegasus pony. Hollow bones made pegasi fairly ineffective at hoof to hoof combat, so they relied much more on weapons with reach and ranged weapons, as well as aerial bombardment. They also put more effort into armor and padding, developing lightweight but effective defensive measures. These larger wings also allowed them to achieve greater heights than modern pegasus ponies, and allowed them to travel much farther distances. In terms of total area, the pegasus nation was the largest of the three. Pegasi also had more feathers than modern pegasus ponies, most notably they would often have a good number of feathers in their tails, giving them much greater control in flight.

Terrans

The Terran species was the most varied in appearance, and may well have contained several subspecies. Their notable differences compared to the other species was, as in modern day, more described by what they lacked, rather than what they had. Still, Terrans were quite physically robust, able to take and give quite a beating, and they had a strong culture for science, making up for their lack in physical advantages with technology. With their strength they were quite proficient in mining, metalworking, and machining, similar to modern minotaurs. They leveraged machines to defend themselves from the other nations and to close the distance, as they would excel in close combat.

One example of a subspecies still present in modern depictions are the Saddle Arabians. Trouble Shoes is also a good depiction of what a Terran would have looked like.

Crystal Ponies

Crystal ponies fall into the same boat as the sea pony version of hippogriffs (Not to be confused with the Griffon/Pony hybrid of the same name) in that they originated from an expeditionary group that would have been utterly destroyed had they not been changed. The Crystal ponies came to be in order to be able to survive in the harsh cold of the frozen north. It is lost to history what exactly caused this change in them, whether a god or some lost magical ritual stepped in to save them, but they would have all died had it not occurred.

Sea ponies have a similar origin, an expeditionary group marooned on a sinking island converted from whatever race they were originally into sea ponies. Given their wings in their land forms, it is likely that this was originally a pegasus colony, which matches the architectural style.

Bonus:

Alicorns

While most modern ponies are hybrids of the original species, the Alicorns could be said to be a true fusion of the three. They possess the stature and magical power of the Unicorns, the wings and agility of the Pegasi, and the strength and tail of the Terrans. They, in this way, represent a perfect unity of the warring species, and often manifest when one overcomes the limitations of their hybrid nature to serve a higher purpose. There are rumors that Alicorns existed before the great war, and perhaps during. Some alicorns are born, and others are made.

Draconequui 

Alternatively, Draconequui are an imperfect fusion of species, parts jumbled and forced together often without rhyme, reason, or symmetry. They represent unions formed out of convenience or desperation, tenuous, chaotic, and unpredictable, and often represent base forces of nature and culture like Discord, Fury, and Avarice. Unlike alicorns, no one is born a draconequis. All draconequui are made either from a creature aspiring to something they should not, and are corrupted by the natural magics (Fury and Avarice), or they are formed directly out of the natural magics to fill a gap (Discord?).