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