One important thing to remember, mostly applicable to pre-20th century research is that spelling was unimportant. The spoken word was more important than the written word - they were pronounced in much the same way, particulary if you consider the parents with their Irish accents talking to the registrar with his Glaswegian accent.
So on that basis I have no problem in accepting McLaughlin as the same name as McLauchlan. There will be a number of other variations to consider Mc/Mac, Lauch/Lach/Laugh/Lagh, lin/lan. That gives you 16 combinations from these parts of words with their variations. There may be others that I have not given here.
Around the start of in the 20th century, spelling became more consistent. The spelling of the name accepted by that family around then is likely to be the spelling that has come down the family since then. Other people of the "same" name will have taken on other spellings of the name, even though they are from the same family line further back.
ADP