Karat applies to gold (as a measure of fineness), and carat applies to precious stones (as a unit of weight, equaling 200 milligrams). A carrot is an orange vegetable. A caret is a proofreading symbol (^) used to indicated where something should be inserted.
Some dictionaries list karat and carat as variants of each other, but that’s just because the words have been confused so often for so long that there’s almost no point in trying to keep them separate. Careful writers can keep them separate, though.
For example, these writers use karat and carat correctly:
The only coins affected in this round of price reductions were the Mint’s 24-karat American Buffalo Gold and First Spouse Gold Coins. [CoinNews.net]
Buyers were offered a range of goods of various sizes and qualities with the largest diamond being a 21-carat diamond. [IDEX Online]
For the final three months of the year, Gemfields churned out 5.9 million carats. [Interactive Investor]