There is definitely a difference in what type of carpet is being cleaned and what level can be extracted. For example; Berber carpets tend to clean very well but normally have reappearing stains in the next few days after they are cleaned. Also, the frieze type of carpet can hold moisture so it must be cleaned a lower psi and done over more frequently or have an air mover readily available to dry after it has been completely cleaned. So there are differences and those should be addresses at the initial phone conversation with customer or when an estimate is being done.The stain will then wick into the towel.
If the stain does not come out or was never removed after a professional carpet cleaning. It is more likely a permanent stain.