We all know the Septims were of the Dragon blood, so they could wear the Amulet of Kings. But were they Dragonborns like our Dovahkiin, or were they something else entirely?

As far as I'm aware, they were different...sort of.

The Dragon Bloods (ie: the Septims), the 'gift' was passed through the generations.

Dragonborn, it seems to be more of a random occurrence. Can't be passed from parent to child it seems.

We know that Akatosh blessed them all with the Covenent....
So they were all probably dragonborn in the skyrim sense but could not wield the voice as they weren't taught to wield it by the greybeards.