The Cut is comprised of several measurements of a diamond’s proportions, arrangement and alignment of the facets, and quality of the polish, which all determine how the facets interact with light.
The Carat is a measurement of how much a diamond weighs. Each Carat is divided into 100 “points”. For example a half-Carat stone is considered a “50 point diamond”. All else being equal, diamond price increases with Carat weight because larger diamonds are more rare, and thus harder to source.
When looking for a diamond, Carat should be used as a guideline but not the determining factor in your selection. Carat is not necessarily the best indication of how large a stone will appear, rather the measurements of the diamond are a more important reflection of “size”.