Not sure what family trees you mean (do beware of online trees as they can be full of errors, often copied from each other) but you are talking about 2 different McCaughern families.
John McCaughern (a common surname in the Rasharkin area) and Mary Ann Boyd had (according extracted births in IGI-
www.familysearch.org):
1. Jane born 24 Mar.1870 Co.Antrim
2. Elizabeth bron 27 July 1872 Dirraw, Co.Antrim (Dirraw is the registration sub-district)
3. James born 11 Jan.1875 Lisnagaver, Co.Antrim
4. Anne Lena born 26 May 1878 Sisnagaver, Co.Antrim (this should be the townland of Lisnagaver)
5. Mary McCaughern born 7 Jan.,1881 Lisnagaver, Co.Antrim
These McCaugherns were Protestant- Church of Ireland or Presbyterian.
Patrick McCaughern and Teresa Mooney (possibly Catholic from their names) had:
1. Teresa born 17 Nov.1864 Portglenone, Co.Antrim (page 111 in civil register)
2. James born 23 Feb.1867 Portglenone, Co.Antrim (page 165 in civil register)
3. Patrick born 4 Mar.1869 Co.Antrim
4. Daniel born 25 Mar.1871 Co.Antrim
5. Catherine born 15 Apr.1874 Co.Antrim
6. Margaret born 9 Nov.1876 Ballymena, Co.Antrim (Ballymena is the registration district).
7. John born 9 Oct.1879 Portglenone, Co.Antrim