Are they all prawns caught in the rivers of Ayutthaya?
You cannot tell from the dish name alone. If you want to know the actual origin and whether they are farmed, ask while pointing at the prawns you will order.
Grilled River Prawns · กุ้งแม่น้ำเผา
If you are looking for a meal to share in Ayutthaya, choose grilled river prawns. The prawns are grilled and the meat picked out to eat, and they go well with rice and other dishes for a group. The price depends on the size of the prawns and the selling unit, so look at the prawns you will order before you choose.

It is a dish where you enjoy the aroma of grilled prawns and the texture of the meat. Try the meat on its own first, then add a little of the sauce served with it. With rice you can enjoy the sauce too.
Ask whether the selling unit is per prawn or by weight.
River prawns are a well-known ingredient on trips to Ayutthaya. If boat noodles are a single-bowl meal, grilled river prawns are a dish to choose for sharing with your companions. You do not need to assume from the name river prawns that they are wild or caught in the rivers of Ayutthaya.
You cannot tell from the dish name alone. If you want to know the actual origin and whether they are farmed, ask while pointing at the prawns you will order.
It depends on the size of the prawns and how they are sold, such as per prawn or by weight. If you get the price of the size and number you choose before you order, it is easier to set the cost of the meal.
If you would like to read more about the food and the regions behind it, these sources are worth a look. Ingredients and cooking methods can vary from one cook to the next.
Sharing image credit: Takeaway · CC BY-SA 3.0