A lot of the variety is to cope with very stringent industrial and transport applications that can subject the fluid to much heavier working conditions for much longer times than we give it. Such applications tend to be enclosed, unlike oiling an open lathe bed and saddle, so the oil needs last a long time.
A warning that does appear from time to time on this forum and relevant here, is to avoid Extreme Pressure oils designed for automotive gear-boxes and differentials. Or rather, be very careful where you use them. Though excellent for such gearboxes, they contain additives that can attack bearing bronzes. (Their intended applications use ball or roller bearings.)
Machine-tools should not be lubricated with grease except if and where specified.
By all means use a grease gun filled with oil though.
I don't have one, but my machines don't seem to suffer from having the sliding surfaces cleaned with old paint-brushes and paper towels, then spread with generous films oil I work in by operating the slides a few times. A bit messy, but more paper towels clean up the surplus.
It's worth oiling the ways under the tailstock too, to aid moving that but also to keep rust at bay.