(a) Upon the death of an employee member which qualifies as a duty death but who does not leave a widow or children under eighteen years of age, there shall be paid to his estate a death benefit as provided in paragraph (d) of Section 18.6 hereof.
(b) Upon the non-duty death of an employee member, there shall be paid to his widow, if living, and if not living, then to the child or children (share and share alike) under eighteen years of age at the time of his death, or if neither widow nor children under eighteen years of age survive him, then to his estate a death benefit as provided in paragraph (e) of Section 18.6 hereof.