Mut'ah marriage is a type of marriage in Islam. It has been mentioned in Quran (Sura 4, Verse 24). Your confusion might be because of misinformation. You can read about this Islamic marriage on many websites including www.al-Islam.org.
The Prophet Muhammad (SAWA) taught the Muslim this type of marriage to save themselves from sinful sexual acts. It was practiced by Muslims during the time of the Prophet (SAWA) and government of Abu Bakr and part of the time of Umar, who banned it admitting that it was allowed by the Prophet himself. Hundreds of Hadeeths mentioned Mut'ah marriage in Shia and Sunni books including Bukhari and Muslim books of Hadeeth.
Mut'ah marriage is similar to permanent marriage in many conditions with few differences. Mut'ah marriage has a Mahr like permanent marriage and can never be allowed with an existing married woman just like permanent marriage.
Mut'ah marriage has a fixed agreed time and it does end by the end of the agreed time. No inheritance between them in Mut'ah marriage nor financial liability of livelihood unless agreed in the agreement of the marriage.
The children from Mut'ah marriage have all the rights of children from permanent marriage.
Waiting period after Mut'ah marriage is two menstrual periods.