stage: [13] A stage (like a stable) is etymologically a ‘standing-place’. The word comes via Old French estage from Vulgar Latin *staticum ‘standing-place, position’, a derivative of Latin stāre ‘stand’ (to which English stand is distantly related). By the time it arrived in English it had acquired the additional connotation of a ‘set of positions one above the other’, and this led to its use in the more concrete senses ‘storey, floor’ and ‘raised platform’.
The specific application to a ‘platform in a theatre’ emerged in the mid-16th century. The sense ‘section of a journey’ (on which stagecoach [17] is based) developed at the end of the 16th century, presumably on the analogy of physical levels succeeding one another in ‘steps’ or ‘tiers’; and the further metaphoricization to ‘step in development’ took place in the 19th century. => stand[stage etymology, stage origin, 英语词源]