Voting is like taking out a loan. Imagine you have a large expense you need to cover. Ideally, you want to pay for things up-front, but sometime you don’t have the money. Say you have a good credit score. You have no good reason to take out a subprime loan, which would be needlessly increase the interest you owe. This is like voting for the greater-evil candidate. But you could take out a loan with more reasonable rate, and still be paying interest, but less. That’s your lesser-evil. Then there’s the third option: if you max out your credit card to buy lottery tickets, you could win and have all the money you need, without owing anything. The chances of this working out, however, are very low, and if you cannot make the card payments, your credit score will take a hit, you lose out on your chance for the good loan, and are forced to take the subprime one. That is your protest vote. A shot in the dark that anyone responsible should avoid.
Say you are a strict vegan, and you find yourself at a steakhouse. All of the entrees include meat. You cannot order one of these and be in line with your views, but you can order some vegan sides as your meal or not order at all. Even in these cases, someone else will inevitably order steak, the practice of using animals is not stopped, but you have made a statement towards that goal. Lesser-evil voting would be like ordering a smaller steak. It goes against what you believe in, but to a lesser degree. The protest vote doesn’t change the outcome overnight, but makes it clear that the lesser evil is not what you want.