Some thoughts
(a) typical pilot PoF courses (like most non-specialist courses anywhere) leave some of the detail out so that the main points are driven home without too much distraction by the nice to know things which are important to the specialist (in this case the aerodynamicists)
(b) the flow is a vortex sheet coming off the trailing edge as well as the wiptip vortex. Within several spans behind the aircraft, the sheet wraps up into the tip vortex .. the
pix linked to in the sticky (at Airliners.net) gives a reasonably good flow visualisation of this consideration. (Apart from that, it's a ripper shot)
(c) the wing tip sails (whatever term you prefer) are used for a range of things such as
(i) getting a bit more effective span without upsetting the airport gate infrastructure or having too great effect on overall wing bending loads reaction design problems. Notional figures are that the appendage is worth around a 70% simple span increase ..
(ii) marketing hype .. if it is on the big bird, it looks even better on the pocket rocket. The bending considerations still come into play
(d) you don't get a free lunch .. so, after market STC fits come with fatigue life penalties on the wing structure
(e) there are plenty of references on the net, including several in the sticky, if you want to get a more quantitative feel for what is going on.