Sportsbooks do not all offer the same kind of promotion, and the differences are not just marketing language, they change the actual math of how you convert each one. Here is what each type actually means.
Bonus bet (also called a free bet, or "bet and get")
The most common structure. You place a qualifying real-money bet, and if it settles the way the promotion requires, you receive a bonus bet of a set value. A bonus bet is not cash, it is a token for one more wager. If that wager wins, you keep the winnings, not the original stake. A $100 bonus bet that wins at even odds pays $100 in winnings, not $200. This is the promo type the classic two-bet method is built around, and it is the one most explanations of matched betting are actually describing.