Nope, it’s the same note with the same sound, whether you’re playing a D sharp or an E flat. (The two names are called ‘enharmonic equivalents.’) It’s a pitch exactly halfway between D and E.
The note has different names because it belongs to a number of different scales, and it plays different roles in each of them. In the C minor scale, you call it E flat because there’s already a D natural in the scale and the next note is F, and the rule is that each letter is used once. E goes between D and F, so it’s E flat.
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