Is Kyne a different spelling of Coyne or are they totally different family lines?

The Mayo surnames Kyne and Coyne are two ways of anglicizing the Irish name Ó Cadhain ("descendant of the wild goose").  The name was also sometimes anglicized as Barnacle, by way of translating the term goose (i.e., a barnacle goose).  There was another, unrelated Mayo surname, Mac Giolla Chaoine ("son of the devotee of the gentle one") which was usually anglicized as Kilcoyne, but sometimes as Coyne.

Records I'm finding could mean a marriage of first-cousins.  Was that common in Ireland?

If Coyne and Kyne are both from the same source then was it a family's choice of the spelling?  A child born of a Kyne father is recorded as Coyne when married (spelling error or choice?)

The anglicized form of a name could vary from generation to generation, or even within the same generation of the family.  Much of Mayo was still Irish-speaking in the 19th century (some parts in the west still are today).  The parish priest generally chose what to write down in the parish register, and the family would have deferred to him (and may not have been able to read or write until later in the century).  The priest, even if Irish speaking, may have been unsure how to write down the sounds of an Irish surname, and how it was done could vary from priest to priest as time went on.  Several examples from my own family in Mayo:  Murtagh and Murtha were used interchangeably, as were McDonnell and McDonald at times.  In one branch the older children were baptized with the surname Curraby, but by the time the younger children were being baptized it had changed to Creaby.

I always thought it was American census takers being unfamiliar with Irish names.
I know in a village map from 1868 in Marcellus NY lists my 2nd great grandfather Tady and his brother Patrick Coyne are both listed as "Kyne". Their shop manifest lists them as "Coin" and they appear in other censuses as "Kine!"