Exercise and training are often used interchangeably, but they have some key differences.
Exercise is any physical activity done for the sake of maintaining, or improving physical fitness. Examples include walking, running, swimming, cycling, rowing, etc.
Training, on the other hand, involves following a more structured program that is more goal oriented often with the purpose of increasing performance of a specific sport or activity. Increasing strength and lean muscle mass over time using a barbell program is a great example of “training”.