S&T vs Electronic/Quant Trading Programs

Current undergrad here, soon starting an S&T SA program at a BB. I noticed the bank I'm interning at distinguishes its S&T program from its electronic trading and quant trading programs. For ET and QT, applicants have to be in some type of grad school (Masters, PhD), while S&T applicants must be in undergrad. 

I'd like to have the opportunity to have a quanty/stat/programming sell-side role in the future (not this summer or right after graduating, but say 3-4 years down the line). Is it possible to start with the general S&T program and then move into electronic or quant trading after a few years, or would it be wiser to consider grad school? I'm a math/stats student with programming experience, if that helps. Would appreciate insight from anyone who's in the industry and familiar with these programs. Cheers.