The whole reason 'bet to protect' is even a term is because it doesn't quite live up to being a full-on value bet as most people understand the term value bet. That is "bet to get a worse hand to call." As I said earlier though, what people call a protection bet is really just a form of value betting...a subset.
For a more clear example: Table folds to you on the BTN and you hold AKo and 3x. BB calls and flop comes 359 rainbow. BB checks to you, then turns his hand face up showing QJo and says plainly, "I will not call a bet." As you have the best hand but are clearly not going to get a call from this obvious worse hand, do you still bet? The answer is of course you do. Instead of betting to collect additional value from an opponent's call though, you are betting to collect the value of their equity that they are now folding to you.
In practice, you come up against situations like this reasonably often. You hold a hand that figures to be best, but that will not be getting called by anything worse. In many of these spots it is still correct to bet because of the value you collect when villain folds. In the above example, villain has about 25% equity (in all-in equity terms). If the pot is $40, then $10 belongs to villain and by betting you collect that $10. If, somehow, villain were to call a $40 bet while having only 25% equity, you theoretically are collecting $30 of their call.