In response to Sara's comment about the Wild Turkey Rye tasting note below, I thought that I would pontificate for a while.
In order for a spirit to be called "straight Bourbon" in the United states, it must be made from a mash consisting of at least 51% corn, be distilled to not more than 160 proof, be aged in charred new oak barrels for not less than 2 years (not less than 4 years unless the age is stated on the label), go into those barrels at not more than 125 proof, and be bottled at not less than 80 proof (Regan and Regan, The Book of Bourbon, p. 212). Straight rye whiskey must meet similar requirements, with the exception that the mash that it is made from must be not less than 51% rye. I'm not sure if it must be aged in charred new oak barrels, but all producers of rye whiskey in the United States except Fritz Maytag at Anchor Distilling Company, who does not label his whiskey as straight rye, do age it in exactly the same manner as they do Bourbon.
So, for both Bourbon and rye, we have 51% of the mash spoken for. What about the other 49%? That's made up of what are called small grains (small because their overall percentage in the mash is low, not because the grains are actually physically small when compared to others). For Bourbon, the small grains are malted barley, wheat, and rye. The last two could technically appear in the same mashbill, but with the exception of Woodford Reserve Four Grains Bourbon, all distillers either use one or the other. For rye, the small grains are malted barley and corn. Different distillers will chose different mashbills depending on the characteristics that they want in the finished Bourbon. If they want it sweet and mellow, they might choose to use wheat instead of rye. If they want it spicy and full-bodied, they would use a big rye component. Wild Turkey likes big and spicy Bourbons, so their mashbill is high in rye, higher than most other distilleries use. Whereas most of the now-closed Pennsylvania and Maryland distillers of rye whiskey used very high percentages of rye, most of the Kentucky rye distillers use rye percentages only slightly over the legal minimum. What this means is that mashbill for the Wild Turkey Bourbons is likely relatively similar to the mashbill for Wild Turkey rye.
But is that why Russel's Reserve and WT rye had very similar noses? Probably not. From what I have read, of the five factors that contribute to the final characteristics of a whiskey (mashbill, yeast used in fermentation, method of distillation, properties of the aging barrels, and the length and manner of aging), the last two are by far the most important. And guess what? Both WT Bourbons and WT ryes are aged in the same type of barrels with the same degree of char and in the same locations. It shouldn't be a surprise that they smell similarly.