What are the differences between Super Saiyan God and Super Saiyan God Super Saiyan? As stated in the title, what are the differences between the two?
Are they supposed to be entirely different or is simply the next stage of the previous?
Super Saiyan God Super Saiyan, or simply Super Saiyan God SS is the
  result of a Saiyan gaining the power of Super Saiyan God and then
  transforming into a Super Saiyan. 
  
  This form is physically identical to the first Super Saiyan God form, overall body structure being thinner and slightly taller. The only difference being that the hair is similar to the Super Saiyan transformation but in a blue color. The aura; as opposed to the red-orange aura the previous God form had, Super Saiyan God Super Saiyan boasts a vibrant, flame-like blue aura. Additionally, electricity discharges around the user, signifying the power increase.
  
  (Source: dragonball.wikia.com)


So SSGSS is the next stage of SSG.