Both whisky and vodka can be made from fermented grains. So is it just a marketing decision which to call it? Generally speaking vodka is clear, odorless and tasteless. And whisky is a brown colour and has more of a bite. Of course there's exceptions.
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 alcoholic fermentation. The distillation process purifies the liquid and removes diluting components like water, for the purpose of increasing its proportion of alcohol content (commonly expressed as alcohol by volume, ABV).1 As liquors contain significantly more alcohol than other alcoholic drinks, they are considered "harder" – in North America, the term hard liquor is used to distinguish distilled alcoholic drinks from non-distilled ones, whereas the term spirits is used in the UK. Brandy is a liquor produced by the distillation of wine, and has an ABV of over 35%. Other examples of liquors include vodka, baijiu, shōchū, soju, gin, rum, tequila, mezcal, and whisky. (Also see list of alcoholic drinks, and liquors by national origin.)
The term does not include alcoholic beverages such as beer, wine, mead, sake, huangjiu or cider, as they are fermented, not distilled. These all have a relatively low alcohol content, typically less than 15%. Nor does it include wine based products fortified with spirits, such as port, sherry or vermouth.
There is no evidence for a health benefit for liquor at any level of consumption. Compared to other types of alcohol, excess consumption of liquor is more strongly associated with harmful health effects.
The mixing of mash ingredients that would traditionally constitute two different type of liquors would still be considered a liquor as long as it is properly distilled after fermentation has occurred.
The mixing of two different types of liquors use still constitute a liquor by principle, such as vodka and whiskey, but would in general be called a cocktail.
However a drink mixed with a liquor and another alcoholic beverage that is simply fermented and not distilled is no longer a liquor but a cocktail
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 molasses. This kind of spirit is usually called rum in other countries.
So, the question if something can be a whisky and vodka at the same time, can definitely be answered with yes.
If you look into grain destillated spirit (in scotland, for example), there is grain whisky. It is made from other grains than malted barley (but can contain this as well, but it's more expensive) and is usually distilled in a coloumn still. This is pretty much the same production method as a grain made vodka. And when you mature it in a cask for 3 years, you could either call it a grain whisky, or a cask aged vodka.
In general terms, vodka is almost pure alcohol and water, with very little inherent flavour.
Whisky starts out the same way, but the final product has a very distinctive flavour (or rather many distinctive flavours, depending upon the maker).
Some of the flavour comes from the fermented malted grain (the equivalent of beer), which is often infused with peat or other smoke. But most of the flavour is absorbed from the burnt wood of the oak barrels in which it is aged for years. Twelve year old scotch whisky literally is left to sit in the barrel for twelve years before being bottled. (Once bottled, it no longer ages.)
Similarly, brandy is made from fermented fruit (the equivalent of wine), and aged in oak barrels.
Rum is made from fermented molasses, and often flavoured with spices during the aging process.
Almost every kind of liquor starts out as something very similar to vodka. It's the flavour that develops during aging that distinguishes them.
That's why, where taxes are low or non-existent, vodka is very cheap, while whisky is still relatively expensive.
Interestingly, both names, "whisky" and "vodka," are derivatives of the word for "water" in their respective 'languages of origin'.
So, one might argue that the major difference between the two is simply a matter of language - but I wouldn't necessarily recommend arguing that in a Whisky bar in the Highlands of Scotland, or an equivalent, vodka-supplying establishment in Rural Russia!
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.
This is probably the closest to what you're looking.
Outside of 'clear' vodkas, there's a whole huge range of flavored vodkas that are given a wild variety of flavor through additions, infusions and other processes - next to more common tastes like cherry, lemon, chestnut or apple, you'll find bread vodka, pepper vodka, horseradish, ginger, chili, and many, many more. Zubrowka Palona is one with smoky whisky flavor - it was vodka aged in the same conditions as whisky, in charred oak barrels. The manufacturer still markets it as a flavored vodka, but at this point there's practically nothing separating it from whisky. And there's nothing that says this process can't be used to flavor vodkas. In the end - you can say every whisky is just a specific kind of flavored vodka.