I see sphere used interchangeably with "ball" in the sense of "open ball", "closed ball", with notation like $B_r(x), B_r[x]$.
I also see sphere used to refer to the boundary of a closed ball, e.g. "unit sphere", but haven't seen a notation to go with it.
Is there an unambiguous term and notation which refers to the boundary of a closed ball and can't be mistaken for the ball itself.