It is like the english words to, too, and two. They all sound the same but mean different things. A C# would be the major 3rd of an A major chord. A Db would be the sus 4 of an Ab sus chord. FYI all the white keys on a piano can also be called by a sharp or flat name. Even double sharps and double flats. It is all to keep the spelling correct in music notation. C# and Db sound the same but are notated differently depending on the context.
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