Why do some motors have both 50Hz and 60Hz on their nameplate, and some do not?
The volts/hertz ratio must be constant within some limit. Only the manufacturer can state that limit. Some manufacturers mark something on the nameplate like 380/440 V 50/60 Hz. That is 7.67/7.33 V/Hz or 7.5 V/Hz +/-1.7%. Marking it on the nameplate is essentially the manufacturer's guarantee that is ok for that particular motor. It is likely that you can operate motors marked only with one frequency or the other at something within a couple of percent of the same V/Hz. There is probably not much risk in doing that, particularly if the motor is not running at rated torque 24/7.
With constant V/Hz, an induction motor should be capable of operating at rated torque over a range of speeds while drawing rated current.