I think you're missing the point. There's the shape and there's the symbol.
An octagon is a shape. A stop sign is a symbol that happens to be an octagon. Inversely, an octagon in the context of street signs represents "stop."
The octothorpe, used in music, represents "sharp." In front of a number it represents "pound." In front of a string on twitter it represents "hashtag."
AFAIK the typographical/visual differences are basically irrelevant. It's just a different symbol with a different meaning in different contexts, all represented with the same shape.
An octagon is a shape. A stop sign is a symbol that happens to be an octagon. Inversely, an octagon in the context of street signs represents "stop."
The octothorpe, used in music, represents "sharp." In front of a number it represents "pound." In front of a string on twitter it represents "hashtag."
AFAIK the typographical/visual differences are basically irrelevant. It's just a different symbol with a different meaning in different contexts, all represented with the same shape.