Near the start of the game, shortly after being summoned by the Greybeards, you can ask Balgruuf what it means to be Dragonborn.

Wulfharth and Tiber were the examples he mentioned, suggesting that Wulfharth is thought to have been a Dragonborn by the Nords. Is this true, or are they mistaken? If true, does it mean anything?

I'd like to think so. Maybe they only call them Dragonborn out of ignorance, because they can steal a dragon's soul and don't fully understand the origin of that power. When in truth, they are Shezarrines, incarnation of doom drum (doom driven?), the snake.

In their tongue, he is Vithkiin. Serpentborn.