Why are the names McDonald and MacDonald spelt differently?

"Mac" means "of", especially "son of". In all of Europe, people outside their homeland would add "of" to their surname, sometimes in the local language and sometimes in their native language. The Irish tended to use O' rather than Mac.

Mac vs Mc. Synopsis: This essay describes the reason why other than nineteenth century migration, there are no O' surnames in Scotland, but there are Mac surnames in Ireland. This debunks the myth that Mac is Scottish and Mc is Irish.
Mac vs Mc a myth debunked - ScottishHistory.com
www.scottishhistory.com/articles/misc/macvsmc.html