'Exercise' is a broader term and can be interchangeably with training or practice, though in this context it means 'physical activity'. Whereas 'Workout' is quite specific to going to the gym. Hope this helps!

They are synonymous. "Workout" started as slang/jargon among body builders, then included many different athletic activities, and finally became synonymous with all exercise.

I would say that the difference between them is that a workout is usually planned, whereas exercise is more spontaneous. For example, when people go to the gym for a workout, they usually have some kind of routine that they follow, like they warm up on a tread mill for 20 minutes, then lift some weights, then go on the spin bike for 20 minutes etc. However, there are lots of ways to exercise, like jogging, swimming, cycling etc. All of these involve moving around to get fitter, but don't necessarily require a set routine.

Just a quick correction, you can say "What is the difference between "exercise" and "workout"?". "To differ" is the verb, "difference" is the noun.