What is the difference between a statistical model and a mathematical model?

Mathematical models explain functional relationship between y and x in non-random or non probabilistic environment. On the other hand, statistical models explain functional relationship between x and y in stochastic/ random/ probabilistic environment. The error term in a statistical model is responsible for introducing randomness.

Mathematical model: y=b0+b1*X
Statistical model: y=b0+b1*X+e

Where y is response, X is a explanatory variable, e is the error term, bo and b1 are regression coefficients.