Difference between smith chart and Z-paramter matrix

I am trying to understand what the difference between the smith chart real and imaginary values and the z-matrx real and imaginary values. Are they comparable, Are they related?

Thanks

Smith Chart is used to illustrate and manipulation any kind of complex quantities that can be impedance,admittance,s-parameters,y-parameters etc..

The Smith chart is basically a polar plot of reflection coefficient S11, with an overlay grid that helps to read the corresponding (normalized) impedances.

The smith chart is a bilinear transform between the S11 and impedance plane, for those that remember their complex math from college.