"leafless plant-organ attaching to another for support," 1530s, from French tendrillon "bud, shoot, cartilage," perhaps a diminutive of tendron "cartilage," from Old French tendre "soft" (see tender (adj.)), or else from Latin tendere "to stretch, extend" (from PIE root *ten- "to stretch").

the popular name of cartilage, Old English gristle "cartilage," related to grost "gristle," from Proto-West Germanic *gristl- (source also of Old Frisian and Middle Low German gristel, Old High German crostila, Middle High German gruschel), which is of obscure origin, perhaps from a non-IE substrate language.

1690s (in reference to both the cartilage and the gland), from Greek thyreoeides "shield-shaped" (in khondrosthyreoeides "shield-shaped cartilage," used by Galen to describe the "Adam's apple" in the throat), from thyreos "oblong, door-shaped shield" (from thyra "door," from PIE root *dhwer- "door, doorway") + -eides "form, shape" (see -oid). The noun, short for thyroid gland, is recorded from 1849.

word-forming element in scientific compounds meaning "cartilage," from Latinized form of Greek khondros "cartilage" (of the breastbone), also "grain, grain of salt, seed, barley-grain," of uncertain origin. This is sometimes said to be from the PIE root meaning "to grind" which is the source of English grind (v.), but there are serious phonological objections and the word might be non-Indo-European [Beekes, "Etymological Dictionary of Greek"]. The body material so called for its gristly nature.