Workout is an application installed on the watch, a native application. Workout is equal to third party applications like Strava or Map My Run or any one of the many other options. The advantage of Workout is that its built in, basic, but works better than other options currently for tracking a workout. In the future, the watch OS2 will allow third party apps to run right on the watch and send their data to the watch/phone Activity app. (Activity is the application on your watch with the circles and a companion app on the phone). Workout also integrates with the Health app on your phone to record the activity as a workout.
Now, Exercise, the 30 minute goal you have in your Activity app is unchanged no matter your settings. You only adjust what you want your daily move goal to be. Move goal is measured in calories and is the red ring. The green exercise ring will move anytime you elevate your heart rate and move. You do not need to start a workout to get credit for exercise or move but if you're going for a walk or run for the purpose of exercise I suggest you do. It will record the activity as a workout which is nice to track.
As you move around during the day, depending on how much you move, you will see credit for the 3 categories of Activity. A brisk walk will count towards your goals.