Whats the difference between Gin, Whisky, Rum and Vodka?

All spirits are made by roughly the same process. Something, generally sugary is fermented, during which yeast convert sugars to alcohol, and then distilled. Distillation is the process of bringing the fermented mash to a warm temperature and collecting the vaporized liquid. More of the alcohol, which has a lower boiling point, will evaporate than the water, so you get your high proof spirit. Some spirits are then aged or undergo some other special process and finally additional water is often added to achieve the desired strength, and the liquor is bottled. The things that change between liquors are what the initial sugary substance is, if and how it is aged, and other special things that happen along the way. Other factors, like the method if distillation, effect the flavor, but don't effect what type of liquor is made.

Gin is distilled grain alcohol that is flavored with Juniper, some say its almost just juniper flavored vodka, and is generally not filtered as much. 

Whisky is grain alcohol that is aged in wood barrels. 

Rum is distilled sugar based alcohol that may or may not be aged. Examples are our Rums here

Vodka is the simplest of spirits and consists almost entirely of water and ethanol. It's distilled many times to a very high proof, removing almost all impurities, and then watered down to desired strength. Since just about all impurities are removed, it can be made from just about anything. Potatoes, grain, or a mixture are most common. Flavored vodkas are made by adding flavors and sugars after the fact when the liquor is bottled.

Whisky/Whiskey is specifically made from grain and is aged in wood casks. The grain is mixed with water and fermented to make beer and then distilled. The liquor comes out of the still white and is very much like vodka, although less aggressively  distilled so with some flavor from the grains and fermentation. The color is imparted by aging in wood casks. Different types of whiskey are separated by the grain they are made of, how they are aged, and specific regional processes. Scotches are from Scotland, made mostly with barley, are smokey from the way the barley is kiln dried. Bourbons are made from at least half corn and are aged in charred barrels which impart caramel and vanilla flavors. Rye is made from rye, and there are plenty more variations.

Gin, like the others made with grain, starts is life as beer, which is then distilled to a high proof like vodka. Aromatic herbs including juniper berries and often gentian, angelica root, and a host of secret flavorings depending on the brand, are added to the pure spirit. The liquor is then distilled again. The second distillation leaves behind heavy bitter molecules which don't vaporize readily, capturing only the lighter aromatics. Appropriately bathtub gin omits the second distillation. Dutch gin is made by including the aromatics in the original fermenting mash and has a different, harsher flavor.

Rum is made by fermenting and distilling cane sugar. Traditionally made from less refined sugar, it contains aromas of the sugar cane. Originally it was an inadvertent by product of making sugar as runoff from the refinery quickly fermented. Like whiskey, some rums are aged, giving them an amber color. And, like other sprits there are regional variations with slightly different processes.

And to be thorough...

Brandy, Armagnac and Cognac are distilled spirit from fruits, most commonly grapes.

Agave liquors, including tequila, mezcal, and sotol, are made from fermented sugars from the agave, a relative of aloes.