Why rheostats have current rating in addition to resistance rating?

A resistor, of which a rheostat is, has a maximum amount of current it can handle. Beyond that value it will start heating up a lot and might burns up. Since, the maximum resistance of a rheostat is fixed so does its maximum safe current value that can flow through it.

Comment'Rheostats' and 'potentiometers' describe applications of variable resistors; they are not alternative Words for variable resistors.