Absolute alignment is impossible; a degree of error will always be present.
Run-out will be present in any rotating system and, depending on the system, the different forms may either combine increasing total runout, or cancel reducing total runout.
At any point along a tool or shaft, it is not possible to determine whether runout is axial or radial; only by measuring along the axis can they be differentiated.
However, a shaft may be more tolerant of axial run-out since the centre of gravity is displaced less.
Typically run-out is measured using a dial indicator pressed against the rotating component while it is turned.