Following on from what Garstonite has written, there are several underlying reasons for surname variations.
If a person cannot read or write, their name is what they SAY it is and the scribe has to record it as best he can. The scribe may read back what he has written and the person will agree. This oral transmission can give rise to even greater problems if the person giving the name has a strong accent.
The current practice of having a ‘celebration’ after a baptism is quite new – within the last 30 years. At the time in question, the late 1800s, it is likely that the infant was taken to church by its godparents and the parents would not attend, and there would be no party afterwards. Thus it would the the godparents who would tell the priest the names of the child. The Catholic community in Liverpool at that time was mainly Irish but from all over Ireland, so there would be many different accents. This would increase the possible number of spelling of any one name. You will be familiar with the variants of your own name.
My local church registers include a marriage
6 Jun 1868, Patricium KEALY, [of] Jericho, [son of] Petri KEALY
[married] Catharinam BUTLER, [of the same place], [daughter of] Gulielmi BUTLER
and I think the baptisms of the family are -
Born; Baptised; Child; Father; Mother
3 Mar 1869; 14 Mar 1869; Petrus CALEY; Patricii CALEY; Catharinae BUTLER
3 Jun 1871; 2 Jul 1871; Maria KEIGHLEY; Patricii KEIGHLEY; Catharinae BUTLER
19 Jun 1874; 28 Jun 1874; Gulielmus KAILLY; Patricii KAILLY; Catharinae BUTLER
13 Jul 1876; 23 Jul 1876; Joannes KELLY; Patricii KELLY; Catharinae BUTLER
18 Sep 1878; 6 Oct 1878; Ricardus KELLY; Patricii KELLY; Catharinae BUTLER
11 Jan 1881; 30 Jan 1881; Joseph KELLY; Patrick KELLY; Catharine BUTLER
13 Apr 1885; 26 Apr 1885; Thomas KELLY; Patricii KELLY; Catharinae BUTLER
All these baptisms were recorded by the same Irish priest, except the one in English which was recorded by a Belgian priest. I suspect that the details of the children were provided by a different set of godparents for each child .
The baptism register for another parish has four children that I think are the same family with surnames written as – Aughtigan; Aughtigan; Octagan; Octigan. If you read these aloud and listen, I think you will hear much the same sound for each.
Your decision about the records being the same person will be a personal one based on the total evidence you can collect.