A tābiʿī (Successor) has a recognized meeting with a Companion but is not established as having met the Prophet. Every condition used for defining a Companion should not be transferred uncritically to this category; scholars distinguish points such as religious status at the time of meeting.
A mukhaḍram lived through both the pre-Islamic and Islamic periods but is not classified as a Companion when a meeting with the Prophet is not established. Living during the Prophetic lifetime is not enough to confer companionship, and narrating from a Companion does not always prove direct hearing.
A hadith qudsī is a report in which the Prophet relates content attributed to Allah. It is not Qurʾān in recitational status or legal properties. “Qudsī” identifies divine attribution of the reported content, whereas “marfūʿ” classifies the level of Prophetic transmission; the categories answer different questions.