In order to cook out of your home, you'll need to a permit from your local health department. Unless your kitchen is built as a commercial kitchen in new construction, it is not likely to pass - pets may not enter, open kitchens would need to be walled off, a separate handwashing and mopping sinks are required, proper ventilation is needed, separate cooling refrigerators and three-compartment dishwashing is required, etc. Proper commercial kitchens can cost around $100,000 to install.
The health department would require audits of your processes from purchasing inventory to storage, preparation, cooling and delivery. You would need special equipment to transport from your home to the client's home to keep food at the proper temperature. You would need a special area to store food inventory and storage containers following health department guidelines.
Cooking in client homes, no health department review is required. There is also no overhead since your client is paying for the groceries. You are coming in to perform a service, then leaving. Your only expenses would be obtaining a business license, website, uniform, and gas to and from the home and grocery store.