As has been said. The informant on both per the clippings was father John, a Weaver and mother Sarah, nee Emerson.
The Townland, civil parish and registration sub-district differ but the townlands are adjacent. Ballymacateer, Maralin = Magheralin in Moira Sub-District & Tullyherron, Donaghcloney in Waringstown Sub-District.
This is in the early days of civil registration.Twins should have a time of birth. If it was a correction to the forname and gender it should have been annotated in the margin of the original and that does not fit with the marriages found. Alternatively he realised had only registered Jane on 7 Apr 1865 and not twin John so registered that on 6th May. BUT the father visited a
different register sub-office with a
different book of births and different Registrar would be my guess. No death before the 1867 birth, however death registration in particular was known to be defective resulting in proceedral revisions 1881. The father John resided in Tullyherron, but the birth/s may have been at the mother-in-laws.
Another small difference is he marked X on Jane's and signed on John's.
I know we are all guessing but why go to the bother of a 'catch up registration' for a pre-1864 birth, or even an 1864 birth, with the same DOB - if anyone needed proof up to that point they consulted the baptism register as was done for some OAP claims after 1908.
All the images on IrishGenealogy are quarterly copies (same as the English ones ordered from Southport) and certified as such at the bottom on loose sheets with handwritten row/entry numbers. GRONI digitised the original bound registers with pre-printed entry numbers (they had no quarterly copies of anything pre-partition). They index 'both' births.
The respective Registrar's made their quarterly copies and the same Superintendent Registrar of Lurgan District, based at the Workhouse, confirmed both were a true copies of entries in their books - which they retained locally until full, then deposited in Lurgan.
7. Facilities for Searches, etc., and Fees.—Certified copies of all entries of births, deaths, and marriages registered each quarter are forwarded to the Registrar-General, General Register Office, Belfast. Those relating to the years prior to 1922 are, however, still in the General Register Office, Dublin. https://www.nisra.gov.uk/sites/nisra.gov.uk/files/publications/1934.pdfThe Townlands within Registration Sub-District maps John Grenham blogs about this month are relevant if zoom in on Co. Armagh then Lurgan
https://www.johngrenham.com/blog/2023/11/09/we-still-give-birth-get-married-and-die-under-the-poor-law/Probably need the baptism and possibly burial registers to confirm the true facts, they weren't baptised Magheralin
https://www.familysearch.org/ark:/61903/3:1:3Q9M-CSMW-F4W3-K?i=561 so perhaps Holy Trinity, Waringstown.