Difference between 一顿饭 and 一碗饭
Your intuition is correct.「頓」and also「餐」are measure word for meals, while「碗」is a measure word for bowls (of rice).

Since「飯」refers to both meal and cooked rice, the statement of how much you ate is inferred from the measure word.



To add: I would suggest that「碗」does not really refer to plate of food, as Chinese does not present meals that way. The western notion of plates of food should be measured by「份」(a share; portion) or「盤」(tray; plate; dish). These two are also used to count Chinese dishes.