What is the difference between a free bet and a bonus?

A free bet is for example if you get €25 to bet with at a bookmaker. If you place the full amount on a match with odds 1,5, you will win €37,50. But the bookmaker will only pay out your winnings (€12,50).

If you receive a bonus for €25, and you place the full amount on the same match, you will win €37,50. You will in other words keep the full amount, as the €25 bonus is credited to you. But bonuses have different roll over requirements, so you might have roll over x times the bonus before you can make a withdrawal. But the bonus amount of €25 is yours.