Most of the confusion is caused by carat and karat because both are associated with jewelry. The purity of gold is measured in karats. Twenty-four-karat gold is 99.9 percent pure, but so soft that it is considered impractical for most jewelry.
A carat is a weight measurement for gemstones: a two-carat diamond set in an eighteen-karat gold ring.
A caret has nothing to do with any of this. It is a mark an editor makes in a document to show where additional material should be inserted.