The Mauqoof Hadith - Hadith Mauqoof means it is traced back to a companion and not all the way back to the Prophet (peace and blessings of Allah be upon him). Although it is only traced back to a companion, sometimes it can have the implication of a Marfu' hadith because a companion saying “This was allowed for us" or “This was forbidden for us" is like one of them saying, “We were ordered to do this," or "We were forbidden to do this," and so on. (Such statements are considered Marfu' with respect to their regulations).
The Marfu' Hadith - Hadith Marfu' means it is traced back to the Prophet, upon whom be peace.
Tadlis in Hadith - Tadlis refers to the case where the narrator uses an ambiguous term that does not tell us if he heard the hadith directly from the one on whose authority he claims to have narrated from. For example, a Mu'an'an hadith is one in which the narrator has used the term 'an', for example, 'an Muhammad meaning "on the authority of Muhammad." He could have heard the hadith directly from Muhammad or someone else, possibly a fabricator of hadith. In both cases, it is permissible to use the term 'an'. Muhammad ibn Ishaq is one such narrator, who used to commit Tadlis. If he narrated the hadith in such a way that it is clear that he heard it directly from the one on whose authority he is relating it, then his hadith is acceptable. The latter narrator is considered weak when he relates in Mu'an'an form because of his reputation as one who committed Tadlis.
The Mu'an'an Hadith - A Mu'an'an hadith is one in which the narrator has used the term 'an, e.g., 'an Muhammad meaning "on the authority of Muhammad."