There is no general definition of what a whisky is.
There are of course special kinds of whisky (Single Malt Scotch Whisky, Kentucky Straight Bourbon, etc.) which are very well defined, but the simple word "whisky" can, unfortunatelly, be pretty much everything. There are "whiskies" from india, for example, that are distilled from ...
You could distill a fermented grain mash multiple times in a still and filter it, getting something that could be called vodka (distilled multiple times and filtered) and whisky (distilled in a still). If you then age it in barrels, it's probably legally both - an aged vodka and a very clear whisky.
Can a liquor be both a vodka and whisky? What's the difference?
The short answer is yes.
Here is what Wikipedia has to say about what constitutes a liquor.
Liquor (also hard liquor, hard alcohol, distilled alcohol, fire water, or spirit water) is an alcoholic drink produced by distillation of grains, fruits, or vegetables that have already gone through ...