In addition to other answers:
How is prostitution different? Truly these 2 things are incomparable.
- In your comments I see you said:
Hardly, its just like saying Mutaa is different from prostitution
because its considered to be legal "among Muslims"
Sex with a non-Mahram becomes is ZINA. Yet it becomes halal/recommended when she becomes your wife. (She becomes your wife by 2 tiny lines of words). Same logic is applied to Mut'ah.
Most important note: How is marriage different from a permanent marriage between Muslims where they haven't done the aqd (عقد) its ceremony as the way the Prophet did? Can't you just say they are a few silly words? Well without those silly words the marriage is considered Zina! With it it's considered Halal and rewarding. My point is we live in the realm of God/Allah. In his realm sayings those words (with the 100% intention of your heart that you approve and mean them) is what makes Allah accept it. Prostitution isn't accepted in the realm of our King, Allah. It has no rules. Permanent marriage or Mutah is accepted by Allah and blessed. How is having 4 wives different from men having for themselves and divorcing the women per agreement? Really not that much.
A prostitute will sleep have intercourse with multiple men, perhaps in the same day or week. Yet for Mut'ah, she can't even touch other non-Mahram men. As a result women of prostitution don't physical and mental issues. (too much sex isn't good for the body, it's never lovely, it get's kind of abusive when the person has paid for it and really demands you to do this and that and may get rough on the women)
- Mutah is also heavily used as a fiance-ship period ie the boy and girl get to know each other, for like 2-3 months. If things were going good, then they make the marriage permanent. This gives the bride and groom a good chance to see if they are a good match and if needed divorce early. (I know non-Shias who have a fiance but not married and still can't touch or see their fiance without hijab. Some of them can't bare it and just remove their hijab.)
- Prostitution is a way of making money. Mutah is not about that at all. It's more about fulfilling needs. He can go to a prostitute and pay to get love or go to women from people of the book or Muslim and simply get love. That itself is a good limitation and motivation. Really do you want to have sex with someone who's paid to make love to you or sex with someone who truly loves and wants you?! Such women aren't women of the street, they are socially acceptable women. In other words prostitution is a business transaction but Mutah is a social arrangement.
- For prostitution there is no agreement. Mutah there is an
agreement and a timeframe specified. Parties have rights.
- For prostitution the mother may not know who the father is. Mutah has
Iddah to avoid that.
- If your entire purpose is to discuss this with non-Muslims as you mentioned (and avoid defamation as mentioned your comments) well brother ask the non-Muslims how many out of wedlock marriages or abortions do non-Muslims have and compare it to Islam. Islam has a far less rate on that. Why because you either don't do or if you do it's religiously legalized. Also in the west, men usually just have fun with the woman as in they're collecting a trophy and then say "women goodbye, I don't think we're a good match. It's not you it's me and say goodbye." Do you know how devastating that could be for a women?! The women won't ever be the same women. In addition the women is entitled to dowry and period of commitment. If a boy is known to sleep with women and walk away from his commitment then he is likely to lost his status quicker and more girls would know of his dirty tricks.
- Mutah is meant as a solution for younger boys and girls. This problem is more common in the west (47% of high schoolers have intercourse). No matter what you do boys and girls get away with it. They're curious. With Mut'ah they can have a protected relationship ie there is a certain commitment period, there are notes they agreed on, the women won't be sleeping with others for a specific period, neither the boy is expected to just drift away before his commitment. (They can even agree to have no intercourse)
A prostitute can be any women. For Mutah if the man is married then he has to seek permission from his wife to sleep with non-Muslim ladies. If the lady is a Muslim then he doesn't need her permission.
Having that said, they both do have some similarities as in a man may just have severe sexual desire and needs them addressed (on a travel, his wife is sick, deceased, in a separation, not getting enough sex). In the long run, masturbation and porn would be reduced. Many studies point out to the issues with masturbation and people will be brought closer, usually a person who needs sex, also wants love and vice versa.
In addition men have been given a great touchstone by Imam Ja'far al-Sadiq.
He was asked about what kind of women are good to do Mutah with?
Imam replied: A lady who listens with heed when you explain
Mutah (it has certain boundaries: time frame, dowry and you shouldn't be with another) to them. ( ie she isn't
the kind of woman who is like "I don't care about this, I just want sex, let's get over with it"... She has modesty but also wants to have a joyful time with a man).
I know of it being a narration but I definitely have not quoted it verbatim
Having said this all I would tell you among Shias, 70% of them do Sighe/Muta'ah just prior to their permanent marriage (only as a fiance period). Roughly 0.01% do Mutah before marriage or some others do Mutah when their wife isn't available or they just want to enjoy themselves. Culturally it's not a common thing to do these days. For married men, being with another woman requires extra devotion, time, money.