They are way, way, WAY different.
They each have their own gods and stories.
They are more different from each other than Roman and Greek myths are to each other. (BTW, there are Roman myths that are different from Greek
myths; it is not always the same gods with different names).
Norse myths have a pantheon of gods and stories that have been recorded in two important Icelandic manuscripts: the two Eddas.
In it there are stories about Thor, Odin, Frey, Freya, Loki and others.
There are also heroes such as Sigurd and Helgi.
The gods live in the sky in a realm called Asgard.
It is generally held that the Norse myths are part of a larger family of myths called Germanic mythology.
The Celts have a much longer history than the germanic tribes, and their mythology is different not only in its characters, but
in the flavor of the stories.
The gods are more vague and there has been a lot of Christian influence in the writings that are left to us.
The bulk of the manuscripts come from Ireland; they include the Book of the Dun Cow, the Book of Leinster
and others.
The gods did not live in the heavens, but here on earth, before the arrival of mankind.
They include such characters as Lugh of the long hand, Nuada of the silver hand,
The Morrigan (war goddess), and the Dagda (good god).
Heroes include Cuchulainn and Finn MacCumhall.
It is too complicated to go any further, this is just a taste.
As long as you do not confuse the two, you guys almost gave me a heart attack!