Are there different words for a circle, and the edge of a circle, which are topologically distinct? The following shape, we would refer to as a circle:
First circle
The following shape we would also refer to as a circle:
Second circle
But these two circles are topologically distinct from one another, are they not? The first circle has a massive "hole" in the middle, and so is really more of a loop in two dimensions. The second circle is a "true circle". But we would refer to both as a circle. In fact, the wikipedia page on circles shows images that mirror the first circle: https://en.wikipedia.org/wiki/Circle
But the first circle is less of a circle object than the second - it's really a loop holding a circular form, or the edge of a circle, or a circle with a hole punched in it, than a circle.
I was thinking about this because of Nietzsche's quote: "time is a flat circle". Would he mean to say that time is a normal, two dimensional circle, akin to the second picture of a circle above? Or that time is a loop, like a piece of flat ribbon, folded back on itself? I tend towards interpreting it as the second option, as that makes more sense: he's saying that in the end everything repeats and there are no beginnings nor endings, just an eternal cycle. But that's more metaphysical, the specific question for this post is whether there are different words for these two, clearly topologically distinct, 2D objects, which we refer to as circles?

In addition to the answers given on "circle" being the boundary of a "disk" in a 2-dimensional plane: In arbitrary dimensions one usually calls the set of all $x$ in $\mathbb R^n$ with $\|x\|\le 1$ the (closed) $n$-dimensional unit ball and its boundary, the set of all $x$ with $\|x\|=1$, the $(n-1)$-dimensional unit sphere. Here $\|x\|$ denotes the distance from the origin.
So the first figure would be a $1$-dimensional sphere and the second a $2$-dimensional (closed) ball.
The names have their origin in the case $n=3$ where the $3$-ball actually is a solid ball as you think of it and the $2$-sphere is just the surface of the ball.
