I think this is one of those things where different places will have different expressions that mean the same thing. In Australia "take out" and "take away" could be used interchangeably. "To go" is also acceptable. An older person might be more likely to say "take out." A person ordering a fancy coffee might want it "to go." By contrast, the opposite could be "have here," "eat in," or "dine in," (which sounds just a little bit fancier because you said "dine") . I think it's just a case of being used to all the kinds of sayings that are out there in the world, in case you come across one. If there is anyone who can add to my list of expressions for dine-in/takeaway, then please do.

In America English, when ordering fast food the cashier will ask, "For here or to go." Meaning are you eating in the restaurant or taking home. Take out is usually when hanging out with friends and you ask, "Do you want take out?" Meaning do you want to order food to eat at home. It's not come to use take away for dining situations. The closest is to tell the waiter you'd like a to go box, in the event you're dining in but can't finish your food and need to take the rest home. Take away is usually used in the context information. My take away from the lesson was...