A Special Position is a very rare Position. A special position (특수 포지션, teuksoo pojisheon) refer to additional roles one can carry besides their primary battle position, so special positions can be overlapped with another position, there is no case in which one only holds a special position without any primary position. In some cases one may have several special positions, and in other cases, one may have none, all depending on the person. 
Note: Every basic Position requires manipulation of shinsu and as such, it is the same for Positions like "Dansul" or "Wonsul". As in: not just Wave Controllers get to learn them.
Known Special Positions
The Guide is considered a Special Position, but it doesn't seem to be a variation of a Main Position. It is a very rare position, and the bearers of this position are considered "blessed" by The Tower.
An Anima controls living beings, commonly Shinheuh.
A Wonsul is able to create a perfect circle of shinsu, causing it to gain much greater strength while retaining the same surface and mass.
Dansul is the ability to, from far away, create an area with an enormously large amount of shinsu pressure.
A special position whose main aim is to protect the Light Bearer and/or Spear Bearer.
A Hwayeom is able to convert shinsu into fire and flames for use.
A Jeonsul is able to convert shinsu into electricity or give it electrical properties.