The dictionary definitions don't really make this clear one way or the other, do they?
Leftover food is (or leftovers are) food that has been set out for a meal that has been neither consumed nor served, and so can be saved and used in another meal. Leftover food is not food or drink that has been served to a person and not finished.
For example, leftover bread can be made into bread pudding. Leftover rice can be made into fried rice. I can take leftover hamburgers and vegetables and make them into a casserole, or leftover sausages and mashed potatoes and make them into a shepherd's pie. On the other hand, there isn't much you can do with leftover eggs besides throw them away.
Now here's where it can be confusing. I can say this:
I would never use leftover food from someone's plate to make leftovers.
You can indeed use leftover to speak of food that someone has left on their plate, but you have to specify it as such. You are then using the word in the broader sense of anything that has been left over: leftover furniture, leftover clothes, leftover space, etc. If you just say leftover food (when speaking of food served at a meal) or leftovers, you are speaking of food that can be repurposed and served at another meal.
Edit: As Laurel mentions in the comments, an exception to this is food that you bring home from a restaurant meal that you couldn't finish, generally for your own consumption later. My comments stand for meals made at home.