What is the relationship between Marshallian demand and Two-Stage Least Squares Estimation Procedure

I was reading Varian, and he gives an example of how to find the quantities demanded using a CobbDouglas utility function with observable data, and a question arose: what is the relationship between this approach and simply doing a two-stage regression for price and demand?

Does the Marshallian demand and the regression approach answer different questions?
Does one solve a problem that the other cannot solve?