Not all the counterparts are completely different. Koume and Kotake are a special case but other individuals like the postman, Biggoron, and the Professor are virtually the same people. It could be possible that there are some perfectly identical Terminian counterparts to Hyrule characters.
Although MM did show us that some of the more exceptional and mysterious characters have the ability to travel between Hyrule and Termina. Such as the Happy Mask Salesman and Skull Kid. Kaepora Gaebora is another strange individual with a lot of knowledge of the world. Who will occasionally help out Link by teaching him things like the Song of soaring and then disappear. The fact that the song he teaches you send Link to an Owl Statue lead me to believe that there is some kind of connection between between the two. As ancient Owl Statues are very common in Hyrule. And they typically have some sort of magical purpose in the story.
Looks a lot like Kaepora Gabora, he even mentions it in the game as his.
Hoo-Hoot! We meet again, fairy child! Have my stone statues been of help?" — Kaepora Gaebora
Owl Statues in Link's Awakening give Link helpful information in what to do, where to go, etc. While the Owl Statues in TP can be moved by use of the Dominion Rod and contain the Ancient Sky Characters for Shad's quest. There has to be some kind of connection with an owl that gives Link information in one game, to an owl statue that gives Link info in another. To An owl statue said to be made in Kaepora's likeness that work with the song of soaring, to owl statues that are important to the ancient sky characters and the City in the Sky.
There is also the possibility that the owl from Link's Awakening is Kaepora Gaebora in another form helping Link again.
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