A private chef is a professional who cooks for one household, every day. They are hired to cook meals and prepare and serve them. They may also live on the premise of the household they are working for.
A personal chef is someone who prepares meals in their own kitchen or out of a commercial kitchen and delivers it to their client. Personal chefs can also be hired either as part of an event, such as cooking for an engagement party or on an ongoing basis, such as cooking two meals per week for a family.