What is the exact difference between a model and an algorithm?

An algorithm is a mathematical formula like linear regression for example. Linear regression (with one variable) defines a line in 2-D space. But the slope and position of the line cannot be determined unless some sample values are available to solve the equation.

This regression line can be represented mathematically as y = mx + a.

Once sample values (or training data) is applied to solve this equation, the line can be drawn in 2-D space. This line now becomes the model with known slope (m) and intercept (a). Using this model, the value of y (label) can be determined for a given value of x (feature).