I think there's some confusing overlap, but it actually does make sense when you get down to it.

Shaman: Partners with the elemental spirits. They speak to the denizens of the planes and bid them to do their calling.

Druids: Intertwined with nature and the forces of Life. Soul-brothers with the spirits of the world.

Druids of the Flame: A strange side effect of druidic bonding occurring in the Elemental Plane of Fire. While the plane is not a true world like Azeroth is, it still has a Life force of its own.

So while both Shaman and Druids of the Flame deal with living fire (of various sorts), the Shaman are speaking to the Fire spirits and working together with them, while the Druids of the Flame are aligning themselves with the Life force of the Elemental Plane of Fire. If anything, the Druids of the Flame may be more akin to Fire Elementals than Shaman.

As for Pandaren (or other Shamanistic races, and Druidism), being a Shaman is about bargaining with sentient forces. Unlike Mages, Warlocks, Paladins, and Priests who are channeling raw power, Shamans talk to the elementals and ask for what they need. Any race willing to develop a partnership with the elements (and meet their end of the bargain) can be Shamans. Druidism is much deeper, and involves aligning yourself with the Life force of the planet. In many ways it's harder, though it's also a lot less risky, as Life isn't going to get mad and turn on you.