About static and stationary spacetime

From Wikipedia:

In general relativity, a spacetime is said to be static if it does not change over time and is also irrotational. It is a special case of a stationary spacetime, which is the geometry of a stationary spacetime that does not change in time but can rotate.

A static spacetime is a special case of a stationary spacetime. In a static spacetime, the metric is constant (like in a stationary spacetime) while space "cannot be rotated", i.e., the spacetime is irrotational (unlike the stationary case).
When visualizing (which can be done only in two dimensions) the two-dimensional static space part of a three-dimensional static spacetime, how must this static space part look? How can you see that it "can’t be rotated"? Is it just that the space is invariant when "rotated", i.e., is the space spherical symmetric? Like the space surrounding a point mass, contrary to a line mass, which would mean that the former is static while the latter is stationary? The line mass can rotate, which means that the spatial metric varies periodically, but the form of the space doesn’t change. Can we say that a static spacetime can’t emit gravitational radiation, while a stationary spacetime can? Does irrotational mean that the torsion is zero?