1. I'd better put less food on my lunch plate tomorrow.

2. I'd better put less food on my lunch tray tomorrow.

3. I'd better put less food on my lunch food tray tomorrow.
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Are they all the same in meaning? Does 'tray' mean 'plate'?

Not quite the same meaning. A plate is piece of china or metal, usually quite flat, on which to put food. Usually it is placed on the table where one is to sit to eat. A tray is a larger, very flat piece used to carry plates or other dishes on, as to the table where one is to eat. So the plate will go on the tray. A tray may carry several plates. In a cafeteria setting, one might choose an entrée (main course), salad, bread, and dessert on separate plates, but carry all of them on one tray. So, plate and tray are not usually the same thing.

#3 above is awkward. Lunch and food are redundant. "lunch tray" would be better way to say it, as in #2.

1 and 2 are fine. 3 is okay, but repetitive.

A tray holds several things -- plate, fork, spoon, glass, napkin, bowl, or whatever you need, but the plate holds only the food you choose.

1. The sentence "I'd better put less food on my lunch plate tomorrow" implies that the person is planning to reduce the amount of food they put on their plate during lunchtime. In this context, "plate" refers to a flat dish usually made of ceramic, glass, or plastic, on which food is served.

2. The sentence "I'd better put less food on my lunch tray tomorrow" suggests that the person wants to decrease the amount of food they place on a tray during lunchtime. A tray is a flat surface with raised edges that is typically used to carry food or drinks.

3. The sentence "I'd better put less food on my lunch food tray tomorrow" seems redundant or awkward, as it unnecessarily repeats the word "food." It would be more concise and natural to say "I'd better put less food on my lunch tray tomorrow."

In general, "tray" and "plate" are similar in the sense that they can both be used to hold food, but they have slight differences. A plate is typically used for individual servings of food, while a tray is often used for carrying multiple servings or a variety of items.