What is the difference between them?
I think radial nodes and spherical nodes are the same, and angular and planar nodes are the same.
Finally, how many spherical nodes are there in a $2p$ orbital?
The wave function $\Psi(r,\theta,\phi)$ of a one-electron (hydrogen-like) atom is seperable as the product of a radial function $R(r)$ and an angular function $Y(\theta,\phi)$
$\Psi(r,\theta,\phi) = R(r)Y(\theta,\phi)$
If $R(r_1) = 0$, there exists a radial node. The radial node is a sphere with radius $r_1$. Therefore the terms "radial node" and "spherical node" are the same.
$Y(\theta,\phi)$ is further seperable as
$Y(\theta,\phi) = P(\theta)F(\phi)$
If either $P(\theta)$ or $F(\phi)$ is zero for a given respective angle value, there is an angular node. However, a angular node is not necessarily a planar node. An angular node could be a planar node or a conical node.
$F(\phi)$ being zero corresponds to a planar node.
$P(\theta)$ being zero corresponds to either a conical node or a planar node (some think of the planar case as a specical case of conical, with apex angle being 180 degrees)
Overall, there will be $n-1$ nodes.
$l$ nodes will be angular
$n-l-1$ nodes will be radial (spherical)