They are pronounced the same and therefore easily confused, but “pallet,” “palate” and “palette” are three very different things.
“Pallet” with two L’s and one T has two main meanings: a platform on which goods can be stacked for transport or storage, and a makeshift bed used on the floor or ground. The latter usage can be found in the biblical book of John, when Jesus commands a paralyzed man, “Arise, take up thy pallet and walk,” and in the blues standard “Make Me a Pallet on Your Floor.”
The “palate” with one L and one T is the roof of the mouth. It is most commonly used in reference to food and taste: a discerning or sophisticated palate, a palate cleanser between courses of a meal, the Silver Palate gourmet grocery and cookbook series.
A palette with one L and two T’s is a flat surface on which an artist arranges and mixes paints. It also refers to a group of complementary colors used in a work of art or design.
There’s no handy memory aid for keeping these straight, so if you can’t remember which one is correct for your purposes, ask your local Literary Life Hacker … or Google.