The Biot Savart law is an expression of the magnetic field produced by a steady electric current. Deriving this law entails starting from Maxwell's equations, obtaining and solving Poisson’s equation for all three components of the vector potential.
The Biot Savart law is an equation that describes the magnetic field created by the current carrying wire and allows you to calculate it’s strength at various points. Biot Savart's law deals with the magnetic field induction at a point due to a small current element. It relates to the magnetic field induction at a point due to a low current element.