Training means practicing to gain more skills. Somebody who plays football practices for the football games against other teams so that his team gets good and wins. The word "training" is usually used when talking about sports, but it is also used for training for a job or in "basic training". Basic training is the practicing for people who want to become a soldier. Training for a job is done in apprenticeships.
Today it is often called a professional development. Training also means changing behavior through learning new requirements and methods and usually requires follow-up testing to determine if the behavior has been successfully changed and follow-up training to insure that the desired behavior has been achieved. These follow-up sessions may be repeated until the desired behavior has been achieved.
Exercise may or may not be part of training. When it is, it is called physical training. It is specific and done to improve one's capability, capacity, and performance; see, e.g., strength training or flexibility training.
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