4.5 Which position columns are used for the cross-match?

Disclaimer: so far VizieR does not make any difference between FK5 Equinox J2000 and ICRS (and converting one system to the other has no effect). Positions labeled as J2000 in VizieR can be either FK5 J2000 for old catalogues, or most likely ICRS for recente catalogues. In practice the FK5 system internal error is of the same order as the FK5/ICRS offset (about 80 mas for the latter).