The word “Celtic” as a brush to define the generic Iron Age or later prehistoric peoples and groups of Europe is generally problematic- albeit it is still a term used as a catch all for this time period, particularly to grab peoples attention for museums, tourism and the like. Firstly, each “group” had a distinct culture, so for example there’s the La Tene cultures, Hallstatt cultures and then the various Iron Age groups of Britain who when the Romans invaded, must have been distinct enough to be named as individual groups. Some of which became more romanised than others. One bit of culture that shows how different these groups is the architecture types. For example, Brochs (large round towers generally built by dry stone construction) are common in Scotland during the Iron Age, but rare/non existent elsewhere. Gallic Walls used to defend hillforts are seen in Western Europe, but again uncommon elsewhere.
As for the name, it comes from (primarily) during Caesars conquest of Gaul in the late 1st Century BC. He describes a tribe, early on, practically at the start of his conquests in Southern Gaul called the Celtae, which had then been misconstrued as a namesake for all the people living in Gaul, Britain & Ireland.
As for the Celtic Iberian cultures on the Iberian peninsula, they again were individual tribes, but did have a shared language- Hispano-Celtic or celtiberian. This is different to the languages that will have been spoken in Britain, in Ireland, in Eastern Europe, Central Europe and Western Europe. In the northern area, they had roundhouses up until the Roman Period- but primarily in this area, again showing how it may not have been unified culturally. However, there were some unifying elements such as a warrior culture, hereditary elites and military aristocracies, Castro fortifications, nations of tribes centred around oppida (like an early city/fortified town or settlement), and similarities in material culture including double edged swords that were then adopted by the Romans.
Whilst oppida can be seen across Europe during this time period, architecturally speaking they were in different formats and constructed differently, and very rare in Britain! Apart from this, the Celtiberian culture is arguably quite different to other Celtic cultures in Europe, although I’d hesitate to use the term Celtic due to differences in architecture, material culture, identity and language!