This is a wonderful question!
The differences between champagne and prosecco is the region it comes from. Champagne comes from Champagne, France (an area about 2hrs hours outside of Paris) and includes hundreds of small and large champagne houses such. These include such well known names as Veuve Clicquot, Moet et Chandon, etc...
All other sparkling wines come from other regions including other parts of France (Vins Petillants), Italy (Prosecco), of other parts of the world (USA, Australia, etc...) these wines are not allowed to be called Champagne, and hence are referred to as sparkling wines.
This is also the reason why Champagne is roughly 5 times the cost of Prosecco or Sparkling Wine.