The Bryne/Burns surname spelling has changed over a period of 400+ years in Ireland.
The causal factor: the Brits wanted to preserve a 2-class system (rich and poor), part of which was accomplished by denying education to those who could not afford private schools.
As a result, until the very late 1800's-early 1900's, a majority of Irish were illiterate.Not only could they neither read nor write, they often didn't know how to spell their names.
To make a bad situation worse, a fair percentage of the census takers and government record keepers were barely literate, and that included some of the RC priests.
Note: There was a period when the RC recorded baptisms and marriages in Latin, and spelling errors can be found there as well.See: Latin Names in English (be sure to scroll all the way down for further translations) http://www.from-ireland.net/names/peop/latintoeng.htmhttp://www.from-ireland.net/names/peop/latintoeng.htm
The Brits hired to be recorders in Ireland often struggled to decipher a name spoken with a heavy Irish brogue. (Imagine being in that position in Scotland!)
The spelling in records can be atrocious, even when an attempt was made to spell a name phonetically.
The misspellings, of course, create havoc in the 21st century when a researcher depends upon software to search for a particular name.
In 1663-65 the common spelling was BIRNE and O'BIRNE.You will find the O' (and Mc) attached to many surnames.
The 1800's saw less BIRNE and BEIRNE spellings, and the O' began to drop off the charts.The more common spellings adopted were BRYNE/BRYNES (rare) and BURNS.Many single family records were recorded in both names depending upon the recorder.
Example: G-grandson of Patrick BIRNE and Grandson of Owen BEIRNES, Patrick BRYNE (b. 1840-41) and his wife had 10 children.Most of their birth certs were recorded as BURNS, two as BRYNE and those two were baptized as BURNS.Both Patrick BRYNE (d. 1890) and his wife died (1904) as BURNS, while one of his brothers maintained the BRYNE spelling.Only one of their 10 children died knowing their correct dates of birth because they used the baptismal cert as ID (the DOB's were incorrect), not their birth certs from GRO.It took diligent research and 50 years to discover that!
If you compare the Civil Parish, PLU and Townlands in all of the above URL's, you'll see where the same families' names changed spelling over time but not all the siblings in one family kept a single spelling all of the time.
One final note.Names are very personal, and we tend to be unyielding about their spelling.A BRYNE may tell you that is the correct and absolute spelling.The records, especially Irish, do not always support that belief.
NOTE: When using the above FHC website and entering parents' names, the mother's 1st name can be a nickname (Biddie/Brigie = Bridget, Lizzie = Elizabeth, etc.) and maiden names can also vary in spelling.The father's 1st name can be abbreviated or a nickname (i.e., Bryan for Bernard, Ptrk = Patrick) and, of course, the Bryne/Burns, et al, surname variations are a consideration.