The question wasn't how a SL ski was different from a GS ski, but how a SL turn was different from a GS turn.
Quick and dirty answer:
Short, quick turns vs long, swooping turns.
A more technical answer to the question can be found in the FIS rulebook, describing how a SL course should be set, vs how a GS course should be set
802.1.2 The ideal slalom course, taking into consideration the drop and the
gradient specified above, must include a series of turns designed to allow
the competitors to combine speed with neat execution and precision of
802.1.3 The Slalom should permit the rapid completion of all turns. The course
should not require acrobatics incompatible with normal ski technique. It
should be a technically clever composition of figures suited to the terrain,
linked by single and multiple gates, allowing a fluent run, but testing the
widest variety of ski technique, including changes of direction with very
different radii. Gates should never be set only down the fall-line, but so
that some full turns are required, interspersed with traverses.
903.1.2 The skilful use of the ground when setting a Giant Slalom is, in most
cases, even more important than for a Slalom, since combinations play a
less important role owing to the prescribed width of the gates and the
greater distances between them. It is therefore better to set mainly single
gates, while exploiting the ground to the utmost. Combinations can be set,
but mainly on uninteresting terrain.
903.1.3 A Giant Slalom consists of a variety of long, medium and small turns. The
competitor should be free to choose his own line between the gates. The
full width of a hill should be used wherever possible.