"Belfast" can mean the city itself or the surrounding area and you really can't assume your family did come from Belfast just because there was a more recent connection. It could easily be that that George Morgan came from somewhere else in Northern Ireland or even Ireland, moved to Glasgow and a child or grandchild later moved to Belfast. If your grandfather was born 1908 then the relatives you mother remembered from Belfast would have possibly been living there in late 1920s onwards (big gap between 1865 married in Glasgow and that date).
Civil registrartion of births in Ireland started 1864 which is too late for George Morgan and Catherine Glass but to find church baptismal records you need to know both their religion and were they lived.
However, Scottish marriage certificates contain lots of useful details such as names of parents so their marriage certificate should get you the names of both sets of parents. See
www.scotlandspeople.co.ukJust for reference here's your thread looking for census and death records in Scotland-
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