All of these criteria are more or less the same. I'm not aware that there is one "standard" criterion. More importantly, I think, is that these numbers obtain for ideal conditions, but real systems will suffer from various imperfections and aberrations meaning that the actual resolution and spot size will be degraded. Furthermore, specific applications may call for a different definition altogether.
The spot size or resolution also depends on the geometry. Hence the resolution of the slit geometry is significantly different from that of a circular aperture. If the optical system in question has some kind of aperture stop that is not circular (say, hexagonal or octagonal) then the spot size will not be circular, and the resolution will depend on the arrangement of the spots.