Celtic mythology refers to the polytheistic religious beliefs of the Celts. The Celts were an Iron Age people who inhabited the British Isles (including Ireland), Scotland, Gaul (now France and the Low Countries), Central Europe, parts of modern Turkey and Italy and the Iberian Peninsula. Celtic mythology varies greatly by region, though there are some things common throughout, for example, the Irish form of the god Nodens is Nuada. The Romans later came into contact with many of the Celtic tribes and assimilated deities into their pantheon, sometimes equating them with Roman or Greek gods.
Gaelic mythology is a term referring to the mythology of the Gaelic-speaking Celts, those being, for the most part, the Celts who inhabited Ireland and Scotland. The mythologies of Ireland and Scotland are often referred to as two separate entities due to some differences (mostly caused by the assimilation of the Picts with the Gaels of Scotland,) but the do share large portions of their mythology. Gaelic Mythology is usually divided into four "cycles:" the Mythological Cycle, Ulster Cycle (formerly the Red Branch Cycle), Fenian Cycle (or the Ossianic Cycle), and Cycle of the Kings (or the Kings' Cycle/Historical Cycle).
The Mythological Cycle is in Irish mythology only; it describes various mythological conquests of Ireland, most notably, those by the Tuatha Dé Danann and Milesians. It comes mostly from a body of text known as the Lebor Gabála Érenn (translating literally as The Book of the Taking of Ireland, though usually known in English as The Book of Invasions.) The Ulster Cycle tells the story of prominent heroes and rulers of Ulaidh. This includes legends associated with those such as Conchobar mac Nessa, Queen Medb and Cú Chulainn. The Fenian Cycle contains the exploits of the Fianna and their leader; Fionn mac Cumhaill. The Cycle of the Kings relates the stories of legendary High Kings of Ireland, such as Niall Noígíallach (Niall of the Nine Hostages), Conn Cétchathach (Conn of the Hundred Battles) and Brian Boruma.
Ireland is one of the regions to be considered part of Celtic Mythology and comes with its own unique myths.