Polynomial function is a generic function in the form (linear, quadratic, cubic, and so on.)
Rational function is a function of two polynomial functions written as a fraction or quotient of two polynomial function in the form :
So the difference is rational function shows a quotient of two polynomial functions.
The graph of a polynomial function is continuous while the graph of a rational function is discontinuous as the denominator will become zero at some point. When the denominator is 0, the function will be undefined, thus resulting to a discontinuous graph.