They are not the same. The term 'Food court' is only used to describe an area inside a shopping mall where restaurants are located. The term 'Dining area' can be used to describe an area in which meals are eaten in a home, hotel, and even a shopping mall. You would use the term 'food court' for the restaurant area in the shopping mall, but you could also use the term 'dining area'. However, you wouldn't use the term 'food court' for the dining area in your apartment or hotel.

Dinning * . I'm not a native speaker but to me they r pretty much the same ...

They are not quite the same, a food court refers to a collection of food vendors usually in a plaza or a mall etc. A dining area is just anywhere designated for people to eat. So all food courts are dining areas, but not all dining areas are food courts.