I often hear one of these words spoken with the pronunciation of the other word.

Problem:
The nouns “cache” and “cachet” are not synonyms and should not be pronounced in the same way.

Explanation:
The noun “cache” means a hidden storage space and is pronounced just as “cash” is pronounced. The French verb “cacher” — which means to hide — is the origin of this noun.

The noun “cachet” means an official seal and is pronounced just as “sashay” is pronounced.

The noun “cache” is accurately used in the field of information technology, for example, to refer to a special portion of computer memory, and it’s accurately used in the military to refer to where weapons are hidden by the enemy.

The noun “cachet” is accurately used in the fashion industry, for example, when describing attractive clothing (e.g., “a dress with the cachet of a top designer”).

Speakers most often seem to get into trouble with these two words when they pronounce “cache” in the way that “cachet” should be pronounced.

Solution:
Use “cache” (rhymes with “cash”) when referring to a store of something. Use “cachet” (rhymes with “sashay”) when referring to something that has a recognized endorsement.