Is it true that in piano the exact sharp of a flat, b flat, and e flat is c,

[Maxwell House Rich Dude]

sharp, d sharp, f sharp, g sharp? I was just wondering because I can play the revolutionary etude by chopin in 4 sharps of c sharp, d sharp, f sharp, and g sharp instead of a flat, b flat, and e flat, with a few adjustments obviously. The same applies for Grand Valse Brilliante.
sorry Grande
When I say exact sharp, I mean exactly one note above every single note in the song.