I sometimes see two or three of these nouns used interchangeably.

Problem:
Most Americans pronounce these nouns in the same way, but they have distinct meanings.

Explanation:
I confess that I do not make any distinctions in pronunciation of these four nouns, but I am sure that some people do.

My excuse for identical pronunciations is that all four nouns have the emphasis on the first syllable, and this makes it more difficult to pronounce different endings differently.

As noted at Wikipedia, identical pronunciation of these four nouns makes them homophones.

Nobody can pronounce the A-T word “carat” — starting with a “c” — differently than the A-T word “karat” — starting with a “k” — but these two nouns do have different meanings.

Here are the definitions of these four nouns:

• “carat” — spelled C-A-R-A-T and abbreviated “ct.” — means a unit of mass for precious stones, equal to 200 milligrams. A five-carat diamond has a mass of one gram. The 3,106.75-carat Cullinan diamond, purportedly the largest rough, gem-quality diamond in the world, had a mass of 621.35 grams.
• “caret” — spelled C-A-R-E-T — means a proofreader’s mark (^) made in written or printed matter to indicate where something is missing. The noun “caret” is the third-person, singular form of the Latin verb “carere”, which means to lack, so there is lacking is the literal meaning of “caret” in Latin.
• “carrot” — spelled C-A-R-R-O-T — means Daucus carota, the name of a species of plant in the parsley family. The origin of “carrot” can be traced to words that meant “horn” or “head”.
• “karat” — spelled K-A-R-A-T and abbreviated “kt.” — means a unit of measure for the purity of a gold alloy, equal to 1/24 part. Pure gold is 24-karat gold; an alloy containing 50% gold is 12-karat gold.

There is a tricky part when it comes to the two nouns that end with A-T. Americans and Canadians favor the “c” word to refer to mass and favor the “k” word to refer to gold purity, but English writers elsewhere often use the “c” word — that is, C-A-R-A-T — to refer to mass and to gold purity.

This means that “24-carat ring” — spelled with a “c” instead of a “k” — could refer, especially outside the U.S. and Canada, either to a ring that weighs 24/200 grams or to a ring made of pure gold.

Personally, I would prefer a “24-karat ring” — with a “k” — over a “24-carat ring” — with a “c”. Buyer beware!

Solution:
Use the fact that “carat” (C-A-R-A-T) comes before “karat” (K-A-R-A-T) in the dictionary and the fact that “diamond” comes before “gold” in the dictionary to remember that the “c” word goes with diamonds and that the “k” word goes with gold. Use the “e” in “proofreading” to remember the “e” in “caret” (C-A-R-E-T). Finally, remember that vegetables rot when writing “carrot” (C-A-R-R-O-T).

I sometimes hear a distinction made between these two nouns.

Problem:
These two nouns are not quite synonyms.

Explanation:
The primary definition of the noun “kind” is group or class of people, animals, or objects with the same character or nature, or identified together together because they have common traits.

The noun “kind” dates back to before 900, when it meant origin, race, or nature.

The primary definition of the noun “type” is a number of people or objects that share one or more characteristics, thereby causing them to be considered to be a group.

The noun “type” dates back to the mid-1400s, when it meant symbol or figure.

Solution:
Prefer “kind” when referring to people. Otherwise, use “kind” and “type” interchangeably.