The Celtic people of Spain are related to the Irish & Scottish Gaels. The Basques speak a non-indo-european language which is not related to any other known language, tho' in grammatical structure it is similar to the Hungarian, Finnish & Turkic languages. The Celtiberians were a mixture of Celtic & Basque tribes, with the Celtic element apparently being the more dominant.
The few fragmentary inscriptions written in the ancient Celtic language spoken in Iberia are clearly goidelic (pertaining to the Gaelic languages of Irish & Scottish Gaelic & Manx). This is also attested by the ancient traditions of the Irish people regarding their origins, which have always maintained that their ancestors, the Milesians in 1700 B.C. (hope I'm right, going by memory here) or so, sailed from Spain & conquered the island.
Before their arrival in Spain, they had sojourned in Egypt & before this they had lived in Scythia, the land of their origin according to the mediaeval Irish historians. The term Celtic signifies the race of Celts in general, whereas Gaelic means the people of Ireland, the Scottish highlands & Hebrides & the Isle of Man in particular.There is a very interesting article in the 1911 Encyclopaedia Britannica on the Celts which goes into great detail, it's well worth reading.