What does it mean that multiple whiskey brands come from the same distillery? Today I was looking at buying my first bottle of whiskey since I got a liquor store gift card worth of $50. I enjoy whiskey so I figured this would be nice to buy. I was looking at for example Blanton's Bourbon and after doing some research, I found out that Blanton's Bourbon is marketed by Sazerac Company and distilled at Buffalo Trace. After looking further, I found out there are only about 13 actual distilleries in the USA which most of them produce multiple brands.

question: 

Take my Blanton's example. What does it actually mean that it is done by multiple companies? Does this mean I can also just buy a bottle of Buffalo Trace whiskey for the same taste and pay less? Also, who gets to decide the taste, if it's different at all? Blanton's or the distillery itself? I'm kind of confused at this moment and before I spend my gift card I'd like to get some clarification of why things are done this way. Right now I feel like the "sub brands" like Blanton just buys from Buffalo and call it their own, I don't want to spend my gift card on a... well... sort of "fake" product that's just a marketing trick, if that makes sense! Hope someone can clear things up for me. Thanks in advance!
A distillery is just a building at the end of a day, the flavor of a whiskey comes from the ingredients and equipment used inside it. In whiskey making the equipment used makes a big difference in the end product, here's a non-exhaustive list:


Stills: stills are used to concentrate alcohol, the shape and material used for stills make a great difference in the end flavor of the whiskey
Barrels: whiskey is aged for years, generally in barrels of some kind. The material used can make a big difference, for instance there's charred barrels, used wine or port barrels. The whiskey will take flavors from the barrel as it ages


The ingredients that are used in whiskey making likewise make a big difference:


Grain: Barley, Rye, Wheat and Corn are all used in whiskey making, and each give whiskey a very different character
Peat: peat smoke is widely used in scottish whiskey making, the amount and type of peat used gives the end product more or less flavor 
Yeast: the strain of yeast used in the fermentation will have an impact on flavor


There's also conditions to consider like the temperature and length of the initial fermentation, still heat, etc. There's the number of times that a whiskey is distilled, triple distillation would give a very different character than double distilling. These are all under control and change the end product. 

So a distiller with a single set of equipment using the same grain could make many different characters of whiskey by varying the process and types of barrel used. If they have different stills and use different grains a single distillery could make a very wide variety of whiskeys. 

As for this specific case, Blanton is a brand which is named after Albert Blanton, one of the founders of the Buffalo Trace distillery and who worked there for more than 5 decades. The same company (Sazerac) owns several distilleries and produces many different brands. For all I know they do just pour standard Buffalo Trace into the bottles and market it as something else, it wouldn't be the first time a company pulled that trick, however that would be bound to be noticed by aficionados and it wouldn't do their reputation any good.