increase degree of a spline

Sometimes I try to INCREASE the degree of spline, e.g. from 3 to 5.

 

Generally I use Fit Curve to do the job. In Fit Curve both ends would be confined by default and I would not do any futher "Specify Constraint" actions. My observation is that the error between the new spline and the original spline is often 0. I wonder whether they are de-facto mathematical equivalents. 

 

Thanks for your comments!