Axes
An axis is a line with a direction: what a profile revolves around, what a circular pattern turns about, what a rotation pivots on, what a helix coils around. The three world axes are always there; axis() builds any other one from an offset, from an edge, or between two axes.
Planes
A plane is a flat reference: the surface a sketch is drawn on, the mirror of a mirror feature, the halfway mark between two faces. Every model starts with the three origin planes, and the Plane tool derives new ones from them or from existing geometry.