"Đĩa" and "Dĩa" have the same meaning.
As with dĩa/nĩa and thìa/muỗng.
Why is it NOT "một CÁI đĩa" and "một CÁI ly"??
You could say một cái đĩa/dĩa or một cái cốc/ly if you want to talk about the plate/dish or glass by themselves but here we're talking about a plate/dish and glass of something.
Why doesn't "đặt" work?