The way I think of it "training" is getting ready for a particular challenge or event like a race, a fight, a sport or a job.
"Exercising" and/or "working out" is more general physical activity for the purpose of getting/staying "in shape" and promoting general good health, but without a particular performance goal in mind.
Most training will involve exercising, but not all exercising is training. Going for a brisk walk on the beach is a way to get some exercise, but it isn't really training. Going to martial arts classes while preparing for a competition is also a way to get exercise and it is also training.
Your example is more in line with what I would consider as exercising because there is no event that is being prepared for. Also, that particular goal will have more to do with what happens in the kitchen than what happens in the gym, but that's another story.