Yes, exactly. The well temperated musical tuning [0] is "good enough". it's an approximation. Some pitches for notes sound almost the same and that's why they today are represented with the same key on a piano.

> For some reason I don't totally understand, some have 2 names (e.g. C#=Db, D#=Eb, F#=Gb, A#=Bb).

[0]: https://en.wikipedia.org/wiki/Well_temperament

Some famous music for the well temperament: https://en.wikipedia.org/wiki/The_Well-Tempered_Clavier