FYI This is information I recieved from a Disney Chat, if anyone else had the same question:
Thank you for contacting Disney. Please hold while we route your chat to a Disney Cast Member who will help you with your question.
Welcome to Disney! My name is Madeline. How may I help you today?
you: I have a question about Disney Gift cards and using them in the parks.
Madeline: Good morning! How may I help you with the Disney Gift Cards?
you: The gift cards that you can purchase at Stop and Shop, can those be used in the restaurants at walt disney world?
Madeline: Are these cards branded as a Disney Gift Card? The reason I ask is that I was not aware that they were sold in a Stop and Shop.
you: They are branded that way yes
you: Stop and Shop sells many different gift cards, iTunes, Chili's, Starbucks, etc.
Madeline: OK. Disney Gift Cards can be used at restaurants at Walt Disney World.
you: Thank you.
Madeline: You are certainly welcome!