Various types of death
These three types of death are commonly referred to by the Theravada commentaries (e.g. AN-a 1.18 aparāccharāsaṅghātavaggavaṇṇanā). A description of them is found in the Vibhaṅga commentary:


  Tattha ‘khaṇikamaraṇaṃ’ nāma pavatte rūpārūpadhammānaṃ bhedo. ‘Tisso mato, phusso mato’ti idaṃ ‘sammutimaraṇaṃ’ nāma. Khīṇāsavassa appaṭisandhikā kālakiriyā ‘samucchedamaraṇaṃ’ nāma.


I wouldn't be surprised if other traditions talked about other types of death, but these are the types of death recognized by the orthodox Theravada commentaries.

In the quote above, sammutimaraṇa refers to when we say "Tissa died." or "Phussa died." (Tissa and Phussa are just common Pali names).