菜(cài) - dish (of food), cuisine; vegetable, greens in Mandarin

菜 (cài) does three jobs. It is a vegetable (买菜, do the food shopping), it is a prepared dish (这道菜), and after a place name it is a cuisine (中国菜, 川菜, 法国菜). Which one is meant is almost always obvious from the sentence.

The measure words differ by sense. A dish on the table takes 道 or 个: 一道菜, 点两个菜. Vegetables in the market are usually uncounted, bought by weight.

The English speaker's trap is 饭 versus 菜. 饭 is rice, and by extension a meal; 菜 is everything served with the rice. So 吃饭 is to eat a meal, while 做菜 is to cook the dishes. Also worth knowing: in gaming and internet slang 菜 has become an adjective meaning rubbish at something, as in 我太菜了.