Laminate counter surface is made from layers of paper melded together. It was first made in the early 1900s and there are many different styles of it. Corian was invented by DuPont back in the 1960s. It is a solid material made of acrylic polymer and alumina trihydrate.
Both laminate and Corian are scratch and heat resistant, but both can be scratched, and with extreme heat, tarnished. Corian is a lot easier to scratch than laminate but because Corian is solid, you can sand out stains or scratches. You cannot do this with laminate.
Laminate is a thin, flexible cover to wood counter tops. It used to be made in small panels that were connected later, leaving seams. Now companies like Formica make larger panels of laminate counter topping with barely any seams.
Corian is a solid material that is generally 38 mm thick. Like granite, it is set onto the counter and can be shaped or polished.
Corian is a much more expensive option than laminate, but it also lasts for a long time. Your budget and how often you redecorate your kitchen might play into which surface you choose.
Corian comes in about 100 different colors and designs. Corian is also bacteria and mold resistant. Laminate has many more color options than Corian, and even a design that makes the counters look like wood.