A getaway is a speedy escape, like the getaway bank robbers make when they flee the crime scene in a car.
The word getaway is so often used for fleeing criminals that it's also a way to describe the vehicle they use: "Follow that getaway car!" A completely different type of getaway is a vacation, like your family's weekend getaway to the Catskills last summer. The "escape" meaning is older, and it originally referred to foxes that eluded hunters.