First, Southernstunna could not talk in better stereotypes if he/she tried. The vast majority of traders aren't nerdy quants who code.
The reason that S&T is grouped together is because banks recruit it together. Depending on the year, you may find that there simply aren't any trading jobs to be filling - nothing to do with the candidate. Second, once on the trading floor, transitioning from sales to trading is not impossible. Your job is to know your client in either, and the best sales people can make their own P&L outside of the traders quotes by knowing the client.
So, there is more overlap in skills than you think. But people will quickly recognize sales or trading favorable characteristics. MBA programs typically self-select sales-people.