Also, because seeing it over and over is starting to annoy me:
Prostitutes:
1)Are paid in cash, not goods or services
2)Have sex with multiple partners a day
3) Limit their interactions with their clients to sex
4)Work of their own free will
Sayu:
1)Was "paid" in being given shelter, nothing else
2) Only had sex with whoever was putting her up at the moment
3) Lived with her respective patron, presumably did everything she does for Satou
4) Literally had no choice in the matter, as being left on the street would lead to her arrest (and presumably return to the family she ran away from for reasons we do not know yet.