ultra-pedantically: that's true with the "well tempered" tuning that is used almost universally. But this is really just an approximation, and one that our ears have grown used to.

Mathematically speaking, B# <> C. On a piano or other instrument that quantizes tones, we have little choice but to go with the approximation. But for violinists and others that can choose from a spectrum of tones, it's possible to hit those tones exactly. Of course, when playing with others, the violin still needs to quantize just to be in tune with the others.