In reality, no such differences exist, the Scots/Irish thing is a myth, it's all gaelic.
"Mc" is simply an abbreviation for "Mac." "Mac" is the Gaelic word for "son." Thus MacGregor (Gaelic mac Griogal) means "son of Gregor" and MacLaren (Gaelic mac Labhrainn) means "son of Laurence."
"Mc" began as simply a printer's abbreviation and sometimes even appeared as M' . The only distinguichable prefix between Scots and Irish ius the use of the O' as in O'Reilly, the O' meaning "grandson of" stemming from the word Og meaning young.
Similar prefix systems for '(son)of' can be found in other languages, such as Dutch (Van / Van der) and Italian (Di). Other languages used suffixes, such as Magnusson in Scandinavia (son of Magnus) and Ivan(ov) in Russia.