c. 1300, "wheeled vehicle," from Anglo-French carre, Old North French carre, from Vulgar Latin *carra, related to Latin carrum, carrus (plural carra), originally "two-wheeled Celtic war chariot," from Gaulish karros, a Celtic word (compare Old Irish and Welsh carr "cart, wagon," Breton karr "chariot"), from PIE *krsos, from root *kers- "to run."
"From 16th to 19th c. chiefly poetic, with associations of dignity, solemnity, or splendour ..." [OED]. Used in U.S. by 1826 of railway freight carriages and of passenger coaches on a railway by 1830; by 1862 of streetcars or tramway cars. Extension to "automobile" is by 1896, but from 1831 to the first decade of 20c. the cars meant "railroad train." Car bomb is attested from 1972, in reference to Northern Ireland. The Latin word also is the source of Italian and Spanish carro, French char.
late Old English wæsc "act of washing," from wash (v.). Meaning "clothes set aside to be washed" is attested from 1789; meaning "thin coat of paint" is recorded from 1690s; sense of "land alternately covered and exposed by the sea" is recorded from mid-15c.
<a href="https://www.etymonline.com/word/car-wash">Etymology of car-wash by etymonline</a>
Harper, D. (n.d.). Etymology of car-wash. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/car-wash