Bag Mitt's or Punch Bag Mitt's as they are sometimes called are designed for punch bag work. You can wear bag mitt's with or without hand wraps depending on the intensity of your workout. Bag Gloves or Punch Bag Gloves as they are often referred to as, are designed to protect your hand's better than bag mitt's for heavy or frequent punch bag work, you also wear hand wraps for extra protection against hand and knuckle injuries, that can be cause by frequent punch bag workout's with out the correct boxing equipment.