[wforfang]

D-sharp and E-flat are two different notes used to describe the same physical vibration for the same reason "father" and "son" are two different words that could describe the same person. It's just a way to communicate contextual relation.

[marton78]

This is false. D-sharp and E-flat have (slightly) different frequencies. Read the article!

[dehrmann]

...in certain temperaments, but not the ubiquitous 12-TET.

[noslenwerdna]

... as thoroughly explained in the article.

[P_I_Staker]

Well I haven't read the article, so IDK