Well, at least here in the US, we use these words:
-Delivery: You call the restaurant and order. They cook your food and deliver it to you.
-Takeout or Carry out: ou call the restaurant and order. They tell you at what time the food will be ready. You go and pick up the food at that time and take it home.
-To Go: You are at the restaurant and oder your food. When it is ready, you take it "to go". Another use is if you are at a restaurant and cannot finish what you've ordered. You can have the leftovers wrapped and take them "to go".