These three tools each use a series of points to create a curve.
Spline by Control Points 
Spline by Fit Points 
Bezier 
For Spline by Control Points, the points act as a guide for the curve; the spline does not actually pass through all of the points. For Spline by Fit Points and Bezier, the curve does pass through each point. These two tools produce similar results; the main difference is the algorithm behind them, and how they are edited.
...