Forward mode automatic differentiation creates a formula for each scalar derivative. If you have a billion parameters you have to calculate each derivative from scratch.

As the name implies, the calculation is done forward.

Reverse mode automatic differentiation starts from the root of the symbolic expression and calculates the derivative for each subexpression simultaneously.

The difference between the two is like the difference between calculating the Fibonacci sequence recursively without memoization and calculating it iteratively. You avoid doing redundant work over and over again.