Hylians and Sheikah
The Hylia people were the ancient race of humans that the Goddesses had as their chosen people. Their appearance was not unlike that of a common human, except for their pointed ears, so long that their weight made them lay almost perpendicular to the head. According to legend these allowed them to hear messages from the Gods and gave them a form of telepathy. Their eyes too, their gaze, were different than ours as all of their senses were more developed; especially their magic skills.
For a long time, the Hylians flourished in their kingdom, Hyrule, but eventually came a time when they begun to decline. Most forgot the old ways and what the Gods had taught them. This resulted in lust for the legendary relic, the Triforce, but few were aware of where it was hidden anymore, and they knew better than to misuse of it. This lust spread to the other races and eventually led to Hyrule's Civil War and then the Imprisoning War. The Kingdom survived, but after these tragic events, the blood of the Hylia people grew so thin they could no longer be called Hylians and their descendant citizens of the kingdom became simply Hyrulians, the wisdom of the ancient ones, only surviving in their few scrolls they left behind. Also countless artifacts of the Hylia survive, among which some that played a very important role in the history of Hyrule, like the Book of Mudora and the Master Sword. In those last days of war, the Hylian society had taken a feudal form. Still it would seem like they've always had a royal family and an order of knights.
In the world of Termina, while preserving their physical traits, the cultural and political decline of the Hylia (or should we say Ikana?) apparently came to pass much sooner, but so did the first signs of their renaissance which could be witnessed in the commune city of Clock Town. Here however, their descendants never adopted the name Hyrulians (not being there an Hyrule Kingdom in the first place) but begun to call themselves humans just as the round eared people from other lands. They are very skilled in clockworks and hold a traditional yearly celebration, the Carnival of Masks to which they give great importance (as masks seem to have a deep influence on the world of Termina).
Back to the world of Hyrule, let us spend some words about a particular tribe of Hylians: the Sheikah.
The Sheikah tribe kept to themselves in their village of Kakariko and came to be distinctively marked by the genetic traits of red eyes and an inborn affinity to shadow magic. Sheikah were thus masters both in the art of magic and that of fighting because of their skills in stealth and a martial art of their own. Typically Sheikah warrior would wear tight clothing to not be hindered in battle and sometimes protective armors or bandages to conceal themselves. Sheikah mages instead supposedly wore very large clothes and possibly turbans. With their abilities, the Sheikah created several magical artifacts of superb quality, such as the Lens of Truth, the so called Gossip Stones or the Magic Sword.
Throughout the Hylians' golden age, the Sheikah always served the Royal Family of Hyrule, but it is rumored that on one occasion the Royal Family betrayed their loyalty and that the Sheikah consequently added a tear to their symbol, the eye of shadows. As a certain fact, after the Civil War of Hyrule the Sheikah were pretty much extinct, their very village being repopulated by Hylians, and soon forgotten. However, very few of them seem to have survived in the ages that followed. Some of these, continued to serve Hyrule (the Royal Family in particular) others devoted themselves entirely to the darkness.
There are no records of this tribe ever existing in Termina (at least, not with a social identity of their own).