Both were practiced at the time of the Prophet and Abu Bakr...

Both were practiced at the time of the Prophet and Abu Bakr and the early days of Umar's rule. But they were abolished by Umar. Thus basically, the above tradition refers to both types of Mut'a which were prohibited by Umar. Moreover, as we gave evidences in Part I, many Sunni commentators have put this very same tradition of Imran Ibn Husain under the commentary of verse of Mut'a marriage (4:24) showing that this Mut'a refers to Mut'a marriage.

It is interesting to know that in Sahih Muslim as well as in the commentaries of Sahih al-Bukhari and Sahih Muslim it is mentioned that the "man" mentioned in the above tradition ("But a man expressed what he wished") is Umar: "A person said according to his personal opinion, and it was Umar." Sunni references: Sahih Muslim, English version, v2, chapter CDXLII, Tradition #2825 Sahih Muslim, Arabic version, 1980 Edition Pub. in Saudi Arabia, v2, p898, Tradition #166.

Also: "The man intended here is the Caliph Umar Ibn al-Khattab." Sunni references: Fat'h al-Bari fi Sharh Sahih al-Bukhari, by Ibn Hajar Asqalani, v4, p177 Sharh al-Nawawi on Sahih Muslim, v3, p364, Dar al-Sha'ab print The reason that in the original tradition, Imran Ibn Husain did not mention the name of Umar is that he was mindful of the bad temper of Umar, and because Umar said he will stone anyone who does that.

It is also narrated in Sahih Muslim that: Abu Nadhra said: Ibn Abbas commanded to do Mut'a while Ibn Zubair forbade to do it. I mentioned this to Jabir Ibn Abdillah and he said: It is through me that this Hadith has been circulated. We did Mut'a (of Hajj and women) at the time of the Messenger of Allah. When Umar was installed as Caliph, he said: Verily Allah made permissible for his Messenger whatever He like and as He liked. And its command was revealed in Quran.

Thus accomplish Hajj and Umra for Allah as Allah has commanded you, and confirm (by reverting to permanent marriage) the marriages of those women (with whom you have performed Mut'a). And any person would come to me with a marriage of appointed duration (i.e. Mut'a) I would stone him. Sunni references: Sahih Muslim, English version, v2, chapter CDXLII, Tradition #2801 Sahih Muslim, Arabic version, 1980 Edition Pub. in Saudi Arabia, v2, p885, Tradition #145.