..."prostitute". Both words are suffixed by "-stitute", but obviously the meaning are quite different. "Substitute" is a conceptual, mental and intelligent activity, whilst "prostitute" is a profitable, body (mostly) and sensual activity. In my opinion, they don't have any reasonable relationships! So why do they spell so similar?
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They are related by situation. Both are derived from the Latin root word, to stand.
One stands before (exhibited), one stands under or next to (in place of).
prostitute: from Latin prostitutus, (expose publicly, as in for sale) from pro-: before + statuere: cause to stand, establish, to put, place.
Used from the 1520s, to offer to indiscriminate sexual intercourse (usually in exchange for money).
substitution: from Latin; put in place of another, place under or next to, present, submit, from sub "under" + statuere: set up, to stand with derivatives meaning place or thing that is standing
Used since late 14c., appointment of a subordinate or successor
All those words derive from Latin statuere, which in turn derives from the word stare (to stand). This goes back to an Indo-European root *sta and so relates to words like German stunden.