As a previous post has said Mc or Mac are simply different spellings of the same thing and has nothing to do with being Irish. The benefits of education allow us to be picky about spelling nowadays but it is only in very recent times that most people had sufficient education to do so. Before that people said their name the way it sounded and relied on an official at immigration or in church records to interpret that sound in a spelt name.
Any Mc or Mac names in Ireland belong to people who moved there from Scotland for many reasons. Both countries are only separated by about 20 miles of sea and there would have been constant travel between them long before the plantation of Ulster. Also clans such as the MacDonalds in Scotland share the same ancestry as the O'Donnells who were a prominent family in North Antrim, just a different prefix in a different country.