I sometimes see these words used interchangeably.

Problem:
These three nouns are not synonyms.

Explanation:
A “palate” — spelled P-A-L-A-T-E — is, when it comes to anatomy, the roof of the mouth. It is also the sense of taste, as in “a meal to stimulate the palate”. This noun dates back to the Latin word “palatum”, which also means the roof of the mouth.

The primary definition of the noun “palette” — spelled P-A-L-E-T-T-E — is an oblong, thin tablet that holds small quantities of paints and that has a thumb hole at one end. This noun comes from French but is derived from the Italian word “paletta” — the diminutive form of “pala”, the Italian word for shovel.

A “pallet” — spelled P-A-L-L-E-T — originally meant a bed of straw but now usually means a wooden frame onto which goods are loaded, as in “The roofing materials were delivered on pallets.” This noun is derived from “paille”, the Old French word for straw.

Solution:
Use P-A-L-A-T-E when referring to the roof of the mouth. Use P-A-L-E-T-T-E when referring to an artist’s tool. Use P-A-L-L-E-T when referring to platform for loading and unloading goods.