Now if this was Arabic music I could understand the difference between Bsharp and C, 'cause they have Quarter-tones. Did Beethoven learn music in the Middle East? Lol.
Actually that's not a bad way to think about it. On a piano, obviously B# and C and everything are the same, however on a violin or trumpet etc. notes are played differently based on how they function. I'll use a different example to (hopefully) better illustrate the point.
Let's take an Eb note, and let's say you're playing a C minor triad (C, Eb, and G). Let's say in another context we're playing a B major triad (B, D#, and F#). Even though on a PIANO the D# and Eb are the same, if a violin were playing those notes they would play them differently due to the context. The Eb would be played slightly lower than the D# tuning-wise. hopefully this is useful to you.
Another thing to consider is the chord you are playing. In a minor piece, when the 7th is raised, if there's a chord accompanying it it is the V chord, or in this case a G# chord. The V chord is always a major triad, and a dominant seventh if there's a seventh (don't worry about that if that's confusing though). Suffice to say the V chord has to have that "leading tone" (the half step below the root, in this case a "B#"). This is why the seventh gets raised. So.... let's say we called the B# a C. The triad would be a G#, C, D#. This doesn't make sense, however, since a triad is stacked thirds. A C and D# is not a third, it's a second. In this case, an augmented second, but it's a second. A G# and C is a fourth. A diminished fourth, but still a fourth. It would actually be more confusing to read G#, C, D# and then realize it sounds differently than it's written.
Basically a triad, in terms of what we name the notes, has to be stacked thirds. So a triad built off of some sort of G (b or #), the next two notes HAVE to be called B and D, sharp or flat.
Suffice to say, this is nothing compared to G# minor. The raised seventh you ask? An F double sharp (enharmonically a G). That's not fun.
If it is played on the same note as a C and it sounds like a C, it's gotta "B" a "C", lol.
