I had no trouble using my regular european adapters in Switzerland, as
long as the base has the pointy ends shown above. Some older adapters,
including previous versions sold in the RS store, had rounded ends and
will not fit Swiss outlets.
Basically a type C plug is a squashed hexagon. I can still remember them being introduced during my childhood. The idea was to make it impossible to plug grounded plugs in ungrounded power strips. So power strips with ungrounded sockets have the same squashed hexagon shape.
Ground sockets in Switzerland also have a squashed hexagon shape, but it is slightly fatter, and it was at one time intended that that would become a world standard.
There are a lot of adaptors around that claim to be type C, but are not. It is not sufficient to have just the two prongs at the correct spacing. It must be the squashed hexagon shape. All appliances in continental Europe that do not require a ground now have that plug.
Grounded appliances in Europe usually come with a plug that fits in the type E or F sockets. But Switzerland has type J sockets, so they won't fit.