Diced means smaller tiny pieces, chopped is either big or small. Diced is less common and can be replaced with chopped, but in cooking, diced is specific to smaller pieces.

They are all different. They indicate different outcomes of cutting a specific way. Chopping is typically larger slices of whatever is being cut, dicing makes very small pieces. To better explain the difference, you would put sliced onions or tomatoes on a sandwich. You would put diced onions or diced tomatoes in a salsa. Also be sure to add in comma's when asking a question where multiple items are being given. So your question would have read like this. "Are chopped onions, diced onions, chopped tomato, and diced tomato. Do they mean the same thing? "