Difference between "exercise" and "workout"

Solution 1:

The following phrase used in the question, sounds stilted and is grammatically incorrect.

I will do workout today NO

A more natural way of saying this would be:

• Today, I'm going to workout (in the gym)
  or
• I'm working out today

The example sentence with exercise although grammatical,

• I will do exercise today

is less common than the following structures:

• Today, I'm going to do some exercise (Google)
  or
• I'm doing some exercise today (Google)

As mplungjan and Josh61 have both pointed out, workouts are usually performed in a gym whereas an exercise can be performed anywhere.

For example, walking is considered a good form of exercise. It is never a workout. So an exercise can be anything: sit-ups, press-ups, going for a jog etc. Any physical sport is considered a type of exercise.

A workout is often a routine performed in the gym, the gym-goer will exercise several different muscles in one intense session.

Solution 2:

The have a similar meaning. Exercise is a more general term for physical activity while workout refers more to a specific set of physical exercises, generally in a gym, which follow a precise pattern.

Workout:

• A session of exercise or practice to improve fitness, as for athletic competition.

• the activity of exerting your muscles in various ways to keep fit.

• 10 Workouts You Can Do in Your Big-Box Gym.

Exercise:

• Activity that requires physical or mental exertion, especially when performed to develop or maintain fitness:

  • "the doctor recommended regular exercise"; "he did some exercising"; "the physical exertion required by his work kept him fit"

Source:http://www.thefreedictionary.com/exercise Source:http://www.thefreedictionary.com/workout

Solution 3:

If you work up a sweat in a gym, I would use workout. It exercises your core and other body parts and helps your general stamina and perhaps makes you lose weight

Anyone can exercise to practice something or to strengthen a limb without becoming sweaty.

I am exercising my right arm to help my RSI for example.

I can also do some mental arithmetic (exercises) to exercise my brain.