The dictionary meanings of those words overlap each other. Simple observation of facial expressions and body language when churches have the signs of the cross made at them or when statues are bowed down to reveals to an observer what most ordinary Catholics are doing! They are paying homage, showing special respect, showing adoration, showing reverence and piety...they are worshipping! Do you think Christ died on the cross just so men could then form images of himself or of Mary so that men should again be in bondage to images of stone and wood? I conflate nothing...you are in denial!
By the same logic, Protestants worship beds when they kneel before them.