The O' and Mac mean "son of" if I got it right. But are they both Celtic or Gaelic.?

Gaelic represents one branch of Celtic. "Celtic" is now a group of languages, like "Romance." The Q-Celtic branch includes the forms of Gaelic spoken in Scotland. Ireland, and the Isle of Man. The P-Celtic branch (no, I'm not kidding--they really are P and Q!) includes Welsh, Cornish, and Breton.

O' and Mac/Mc are both Gaelic. Mac or Mc means "son of," and O' (from "ui") means "grandson of." O' is seldom if ever used in Scotland, and Mac is more common in Scotland than in Ireland. Mc is used in both, although some people contend that Mac is Scottish and Mc Irish. (Anyone who had an uncle named Charles Edward McIntosh knows better!)

The Welsh equivalent was once Mab or Map, but it has now become ap, uncapitalized, and is found mostly in last names beginning with a p that could be removed and still leave a name--e. g. Pugh is ap Hugh, Price is ap Rhys, and Pritchard is ap Richard. In the case of a Welsh name beginning with a double L, the p mutates to an f and replaces one of the l's, so that ap Lloyd is Floyd.

These are terms in the Gaelic (Irish) language. BTW, I think O' means "grandson of".

Celtic is a cultural term and the Irish are thought to be one of the Celtic peoples.

"Mac" means "Son" in both Scottish and Irish Gaelic. The O' prefix - which means "from the clan/tribe of" or "descendant of" is only used in Irish names, not Scottish names.

The female form of "Mac", used when Gaelic is spoken, but not when the names is "Anglicised" is "nic" in (in both Scottish and Irish Gaelic) and the female form of "Ó" in Irish names is "Ní". Where an Irish woman takes the name of someone whose name begins with Ó by marriage, she becomes Bean Uí or simply Uí.

So in Irish: Brigit O'Donal: = Brigid Ní Dhónaill, if it is her own name, and Brigid Bean Uí Dhónaill if it is her married name.

Mary MacGerald - Máire Nic Gearailt, or if it is her married name: Máire Bean Mhic Gearailt

Things are not *quite* that complex in Scottish Gaelic names: Catherine MacPhee is properly called in Gaelic, Caitrìona Nic a' Phì.