I cannot speak for SS, hopefully he will drop in to give his thoughts.
My thoughts are the first born Margarite baptism found by SS, reply # 1, died before 1875 as another Margaret was born illegitimate after the death of John Smith. James Burns (second husband, married 1879) maybe her father, but only Mary baptised her as Burns, (found by John, reply #51) But she used the surname Smith.
Up until 1875 registration was not enforced, but could be frowned upon by some officials, if the child was not registered. Many saw baptism as enough, as god was more important, Catholics in particular.
The cert very generously purchased by SS, is either another John Smith/Mary Byrne, or the priest/official was on their case and the birthdate was altered not to incur a fine maybe. (6 wks to register from birth)
Just my thoughts, but stand to be corrected.