When you snap back from something, you get over it right away. An Olympic gymnast hopes he can snap back after a loss and win the next few events.
When someone snaps back, they get right back on their feet, quickly recovering from an injury, disappointment, or setback. After minor surgery, your dog might be groggy for a few hours and then snap back, ready to chase squirrels again. And if you don't study for a math quiz, you may get a bad grade only to snap back, scoring an A on the next four quizzes.