As a general rule the spelling of names in these trees reflects what is actually recorded on the individual’s birth or baptism/christening record, where it has been discovered. This may differ from the usual spelling of the persons name, or from the name on later documents such as a marriage or death certificate, or from a name commonly used later by the individual or the family, or indeed from the spelling of other family members surnames!
For older records the spelling of names was often entirely in the hands of whoever was recording them and widespread illiteracy meant that variations and errors in spelling names was inevitable. Apart from this, the spelling of names often changed over the years with obvious examples (from these trees) being the dropping of O’ from Irish names like O’Sullivan and O’Mara, or surnames like Greg morphing into Greig and Grieg. In Ireland, Fullerton is spelled typically that way, in Scotland it was typically spelled Fullarton. Gouldthorp was variously spelled Gouldthorpe, Goldthorp, Gooldthrop, and Goldthorpe, for example. Keleher could become Kelleher, Keller or Kellar. McLusky could be McLuskie or McLuskey and so on. One branch of the family started out as Lorentz in Germany, but this became anglicised to Laurence and Lawrence several generations after they fled persecution and settled in Ireland (then the USA, Canada, and Australia).
If you cannot find someone you are looking for, look for variations of the surname, or start with someone else in the same family.