I'm a little confused about the definition of the Torus. A geometric definition of the torus could be (Pollack, differential topology):
A Torus is a set of points in the space at distance $b$ from a circle of radius $a$ in the $xy$ plane.
Another geometric definition is:
A torus is the surface revolution of the circle $(x-a)^2+z^2=b^2$ around the $z$-axis.
In the case $b\leq a$ I prove the equivalence of the definitions.
Nevertheless, in the case $b>a$ I think that strictly speaking this is not true, because by definition, the distance from a point to a set is the infimum of the distances from this point to all the points in the set. It is well known that when $b>a$, we obtain a self-intersecting torus with the second definition. However, in the first definition we only obtain the outer surface that we obtain with the second definition.
Am I right?
tl; dr: In a word, yes you're right.
In more detail, every point $p$ of space lies in a longitudinal plane (i.e., containing the $z$-axis), say $P$. (Points on the $z$-axis do not uniquely determine $P$, but we may pick the $(x, z)$ plane for definiteness.)
Since $P$ is perpendicular to the $(x, y)$ plane containing the central circle (gray), the distance from $p$ to the central circle is the distance from $p$ to the intersection of $P$ with the central circle.
In a longitudinal plane we have this diagram:
If $b < a$, the circles of radius $b$ about $(a, 0)$ and $(-a, 0)$ are disjoint; if $b = a$ these circles (blue) touch at the origin. In either case, the union of these two circles is the set of points at distance $b$ from the two-point set $\{-a, a\}$.
If $a < b$, the circles of radius $b$ about $(a, 0)$ and $(-a, 0)$ have two points in common. The union of these two circles (green, including the dashed arcs) properly contains the set of points at distance $b$ from the two-point set $\{-a, a\}$ (bright green), but points on the dashed arcs are at a distance strictly smaller than $b$.