Firstly, they are grammatically different. 'Food' is nearly always uncountable (food/some food), whereas 'dish' is countable (a dish, some dishes).
Food is a general word to refer to fuel for the body. People eat food, animals eat food. You can even give food to a plant to help it grow better.
A dish is a set of ingredients combined and prepared together to make a particular speciality. For example, 'kofta' is a famous Turkish dish. You might say 'The food in that restaurant is very good. You can get a lot of lovely Turkish dishes there'.
I hope that's all clear.