The difference between bonus or Bonus and deposit wagering is how the wagering is calculated, and how the bonus is played. Having to wager just the bonus often means that you will play with your cash first. Once your real-money balance is used up you'll plat with the bonus. You may be able to give up the bonus as well if you win with your cash balance.
A bonus plus deposit wagering is higher, and casinos with such bonus usually don't allow for cash winnings to be paid out. You'll commit to receiving the bonus and keeping it. The wagering is usually much higher for this type of bonus.