Sandwich(also refered to as Laminate)-is any ski built up using layers of stuff(stuff is a technical term used to cover all materials in the core of a ski ie.aluminum alloys,wood,carbon fibre/kevlar,fibreglass,microcell(Rossi),densolite(Atomi c),etc.It is possible to have a sandwich ski with vertical sidewalls,angled sidewalls or even a cap. Sandwich skis skis tend to be more stable and have therefore been used as the foundation of most GS,SG,DH skis.
Cap-introduced by Fischer(stolen by Elan,Salomon and others).Where the external stucture of the ski gives it integrity. Basically an external torsion box(where the core of the ski is wrapped in various forms of fibreglass). Because a cap or torsion box wants to return to its original shape skis made like this tend to be very lively but unstable at high speeds(traditionally t-box skis have been SL or bump skis). When all the companies jumped on the "cap" bandwagon it became apparent that for some skiers the cap was great but other were unimpressed with directional or straight line stability(hence the proliferation of various doodads attached to the topsheets of cap skis to keep the tips on the snow).
Volkl and Rossignol both introduced hybrids that combine the best of both worlds, and Atomic developed Beta to solve the stability problem.
Why caps are still prevalent at the high end in public speed skis is beyond me, but I remember talking to a factory manager that told me that when they started making caps their production was increased because the caps came out of the molds easier than the old square skis.
I do always enjoy the power to the edge argument, if that was all that mattered we would all be skiing Look/Rossignol bindings because of their longer toe wings and 3 points of contact at the heel.