A personal chef is essentially a professional chef who prepares meals for a customer or a family. This can happen in the customer's home or in the chef's own kitchen. A private chef, on the other hand, is a chef who works in a private home, usually for a single client or family. Personal chef work also involves cooking meals for families and private events, but a personal chef will have many clients compared to a single household staffed by a private chef. Private chefs work independently in private homes and on yachts, creating meals that fit the tastes and possible dietary restrictions of family members.
A private chef works full time for a client in their private residence, whether it's a house, a hotel or a yacht.