Solid surface is the High quality building material. By default it is known or called as Corian. Corian really was a brand named coined by Dupont ( American company ) which was inventor or Acrylic Solid Surface material.
These terms are highly used interchangeably. Your designer/carpenter will keep referring you Corian but what he means is Solid Surface material. He/She may not be talking about actual Corian brand ( Dupont product).
The real term is Solid Surface. Corian was the first brand that was introduced in the world. They had patent for almost 15 years so nobody else could make it. This is same example like Colgate. People refer all toothpaste products as Colgate. All photocopy machine is referred as Xerox machine, although Xerox was name of a particular company that was first to invent it.
Acrylic solid surface is the Solid Surface which can bend. Corian, LG solid surface, Tristone Solid Surface are popular ones. There are many Non bending options in Indian market which usually get imported from Chinese manufacturers or are locally manufactured.
About 10 or so years back Patent rights got over & many companies other then Dupont launched their solid surface products. In India Solid surface got introduced 14 – 15 years back, but was used for extremely high profile projects back then.
According to me in last 5 years Solid Surface has gone mainstream. Before this it was just limited to few high end projects and a few architects who were aware of it. It was way costlier then how it is priced today.