【eat away】 —eat continuously; eat as much as one likes:

• Be prepared to spend at least two hours chatting and eating away, relishing every minute of Fran’s delicious German cooking.

Note: The expression does not correlate in meaning with the phrase 【eat away】 from home—have one’s meals in cafeterias, etc.

rather than at home:

• When eating away from home, people eat either larger quantities or higher calorie foods.

【eat out】 —eat in a restaurant, etc. instead of at home:

• Sometimes eating out can be cheaper than buying a weeks worth of groceries.

Cf.: eat in—eat or dine at home:

• I would certainly recommend the hotel to people who prefer to eat in and cook for themselves.