Both Karat and Carat are terms to indicate a quantity. But they refer to a different material.
The term “Karat” is used to indicate the purity of gold. The scale to indicate the quantity of this precious metal is divided in 24 parts. The more parts of the 24 consist out of gold, the more pure the gold will be. The purest form of gold is indicated with 24 karat. In this case 24 parts of 24 are pure gold. When we talk about, for example 18 karat gold, 18 parts of this precious metal exist out of pure gold, the other 6 parts are an alloy. This means 18 karat gold exist for 3/4th or 75% out of pure gold. 
Carat on the other hand indicates the weight of a diamond or other gemstones. In ancient times a carob seed was used as a reference to weight a diamond cause these seeds always had the same weight namely 0,2gram (1/142 of an ounce). Therefore a 1 carat diamond weighs 0,2 grams. This carat scale is divided in 100 points. So mostly when we talk about diamonds smaller than 1 carat, we talk in points. For example a diamond of 0,78 carat is a 78 points. Diamonds that are bigger than 1 carat are referred to in carats.
