If you're from Texas, you'll think of a rifle. If you're from Russia, you'll think of a computer hard drive. I live in both places and it never occurred to me to wonder if the two were somehow connected.
The story I recently heard in Russia is that the same Winchester rifle folks also made hard drives back in the day. Stranger things have happened, but this particular business diversification never took place. A wee bit of fact checking revealed that the Winchester hard drive was actually released by IBM in the 70s and got its nickname because it was intended to have two 30 MB spindles, which reminded someone on the project of the Winchester 30-30 rifle.
In Russian, винчестер (vinchester) is a generic term for any hard drive and is often cut back to винт (vint), which happens to be the word for "screw" (as in the screw that propels a submarine).