pallet (n.1)

"mattress," late 14c., from Anglo-French paillete "straw, bundle of straw," Old French paillet "chaff, bundle of straw," from paille "straw" (12c.), from Latin palea "chaff," perhaps cognate with Sanskrit palavah, Old Church Slavonic pleva, Russian peleva, Lithuanian pelūs.

pallet (n.2)

"flat wooden blade" used as a tool by potters, etc., early 15c., from Middle French palette, diminutive of pale "spade, shovel" (see palette). Meaning "large portable tray" used with a forklift for moving loads is from 1921.