arbor (n.1) Look up arbor at Dictionary.com
c. 1300, herber, "herb garden, pleasure garden," from Old French erbier "field, meadow; kitchen garden," from Latin herba "grass, herb" (see herb). Later "a grassy plot" (mid-14c., a sense also in Old French), "shaded nook, bower formed by intertwining of trees, shrubs, or vines" (mid-14c.).

Probably not from Latin arbor "tree" (see arbor (n.2)) though perhaps influenced by its spelling; the change from er- to ar- before consonants in Middle English also reflects a pronunciation shift: compare farm from ferme, harbor from Old English herebeorg.
arbor (n.2) Look up arbor at Dictionary.com
"main support or beam of a machine," 1650s, from Latin arbor, arboris "tree," from Proto-Italic *arthos, which de Vaan derives from PIE *herdhos "height, uprightness," from root *eredh- "to grow, high" (see ortho-).