In the name of Allah, Most Compassionate, Most Merciful,
The jurists (fuqaha) state that observing a waiting period (idda) is necessary for a woman in the event of her marriage being corrupt (fasid), but not necessary if the marriage was invalid (batil).
Imam al-Haskafi (Allah have mercy on him) states:
“The waiting period (idda) for a woman whose marriage was corrupt (fasid) is.., hence there is no waiting period in an invalid (batil) marriage…” (See: Radd al-Muhtar ala al-Durr, 3/516)
It is stated in al-Fatawa al-Hindiyya:
If the marriage was corrupt (fasid), the judge (qadhi) will separate the couple. If he separates them before consummation of marriage, no waiting period will be necessary, even (if the separation was) after the couple remained in seclusion (khalwa). However, if he separates them after consummation of marriage, the woman will have to observe the waiting period (idda) from the time of separation. The ruling is the same in the case of separation taking place without the Qadhi’s judgment (i.e. the couple separate themselves). (al-Fatawa al-Hindiyya, 1/526)
One should also remember that there is no waiting period (idda) in the unfortunate event of a woman committing adultery and fornication. It is stated in al-Fatawa al-Hindiyya:
“A waiting period (idda) is not necessary upon a woman who committed adultery. This is the position of Imam Abu Hanifa and Imam Muhammad (Allah be pleased with them both), as mentioned in Sharh al-Tahawi.” (al-Fatawa al-Hindiyya, 1/526)
In light of the above, a waiting period (idda), related to marriage, is necessary upon the following women:
1) One who entered a perfectly valid (sahih) marriage and then got divorced after consummation or after being in seclusion (khalwa) with her husband,
2) One who entered a corrupt (fasid) marriage and then separated after consummation (and not merely being in seclusion),
A waiting period (idda) is not necessary upon the following women:
1) One who entered an invalid (batil) marriage and then separated,
2) One who entered a corrupt (fasid) marriage and then separated before consummation, even if the separation was after being in seclusion (khalwa),
3) One who committed adultery,
Now, this leaves us with the definitions of a corrupt (fasid) and an invalid (batil) marriage, and the difference between the two.
Allama Ibn Abidin (Allah have mercy on him) states in his renowned Radd al-Muhtar, quoting from al-Bahr:
Every marriage regarding the permissibility of which scholars have differed such as marrying without witnesses, (will be considered corrupt/fasid), hence consummation of such a marriage would necessitate a waiting period (idda). However, marriage with a married woman or a woman observing her waiting period (due to divorce) would not necessitate a (new) waiting period (idda) in case of consummation, if one was aware that she was already married, as no one has deemed it (i.e. marrying a married woman) permissible, hence the marriage was not establish from the outset. (Radd al-Muhtar, 3/516)
Imam al-Tahtawi (and not Tahawi) mentions that an example of a corrupt (fasid) marriage is marrying without witnesses, and the example of an invalid (batil) marriage is to marry a married woman knowing that she is married or marrying without proper words of offer and acceptance. (See: Tahtawi ala al-Durr, 2/221)
In light of the above, we can conclude that the difference between a corrupt (fasid) marriage and an invalid (batil) marriage is:
Corrupt (fasid): That which there is a difference of opinion amongst the various Sunni Mujtahid Imams regarding its permissibility or otherwise such as marrying without witnesses, as Imam Malik (Allah have mercy on him) is of the opinion that having a specific number of witnesses is not a necessary condition (though it is necessary to publicize the marriage as much as possible), and also a contract where the corruptness is not in its essence.
Invalid (batil): That which is invalid and forbidden according to all the Mujtahid Imams, and where there is a fault in the essence of the contract, i.e. something is wrong with the offer and acceptance or the actual people marrying such as marrying a married woman.
The case with temporary marriage (mut`a) is that, firstly, all of the Sunni Schools of Islamic law are in agreement that a temporary marriage (mut`a) is both forbidden and invalid (batil), hence no (Sunni) Imam is of the opinion that it is permitted.
Imam Kamal Ibn al-Humam (Allah have mercy on him) states:
“The prohibition of Mut`a is final, and there is no difference about this between the Imams and scholars of the lands, except some Shi`a.” (Fath al-Qadir, 3/249)
Secondly, in Mut`a, there is a fault in the actual offer and acceptance, in that it is contracted with the words denoting enjoyment, and on a temporary basis.
Due to the above two reasons, a Mut`a arrangement would be considered invalid (batil), i.e. no Mujtahid Imam permitting it, and the corruptness being in the essence of the contract.
This is the reason why almost all of the books in Hanafi Fiqh state that a Mut`a marriage is invalid (batil), and not corrupt (fasid). Sexual relationship in a Mut`a arrangement would be tantamount to adultery.
Imam al-Marghinani (Allah have mercy on him) states in his renowned al-Hidaya:
“Mut`a marriage is invalid (batil). It is when one says to a woman: “I will enjoy you for such-and-such time for such-and-such amount of money.” (See: Fath al-Qadir on al-Hidaya, 3/246)
Therefore in conclusion, a Mut`a arrangement is invalid and akin to committing adultery. In the event of an invalid (batil) marriage, the woman does not have to observe the waiting period (idda), hence, there will be no Idda necessary after separating from a Mut`a arrangement.
And Allah knows best