In short, silicon is a naturally occurring chemical element, whereas silicone is a   substance.
Silicon easily bonds with oxygen and is rarely found in nature in its pure form. You've likely seen silicon as silicon dioxide or silica, better known as quartz, which is the most common component of sand.
Silica also comes in other mineral forms, such as flint, jasper and opal. When silicon and oxygen mix with reactive metals, the result is a class of minerals called silicates, which includes granite, feldspar and mica.
As silica, silicon is a key ingredient in bricks, concrete and glass. In its silicate form, the element is used to make enamels, pottery and ceramics. This mineral is used in abundance in the ceramic industry in clay and glazes.
Silicone, by contrast, is a synthetic polymer made up of silicon, oxygen and other elements, most typically carbon and hydrogen. Silicone is generally a liquid or a flexible, rubber-like plastic, and has a number of useful properties, such as low toxicity and high heat resistance.