Mc and Mac means "Son of". "O'" means "Grandson of". ie: O'Neil.
Generally, the Irish used "Mc" and the Scottish used "Mac". ie: McKay vs. MacDonald. This is not a rule.. but a generalization.

I have my Scottish and English traced back to early medieval times, them being royalty made it a cake walk. The Norweigen invasion(s) introduced the concept of Sir (last) names. IE: When I traced my lineage to before the invasions.. I got "John, Son of John".. not John Hutchinson, for example.