Taj Mahal is a Tomb made as a tribute to Mumtaz by the great mugal Emperor Shah Jahan....this is as per the written history...
archeological survey of India has pointed out with evidence that the presently known Taj Mahal was earlier a shiva temple(before the Mughals Invaded)....then it was captured by the mughals and all the Idols and statues were mutilated,beheaded and destroyed as they have done with many ancient temples(another example is the elephenta caves).
After a period of time it was again reworked upon and was named the Taj Mahal....it is also said that the architect who masterminded the rebuilding was blinded by shahjahan's soldiers....
finally.....it is Taj Mahal and not Thaj Mahal