True.
But I wonder is there any different belief systems between Celtic Christianity and other denominations. Do they venerate certain saints or have certain beliefs?
"Celtic Christianity" denotes the Christianity practiced in Ireland and early Scotland from the 300's or so until the time when the local Celtic church was fully subsumed by its larger parent Latin Church. The beliefs of Celtic Christianity would have been the same as Catholic and Orthodox Christianity pre-Great Schism. Celtic Christianity, like Coptic and Byzantine Christianity, laid a great emphasis on monasticism; the Irish almost singlehandedly evangelized all of Western Europe that remained pagan, including the German tribes. Many of the great monasteries in France owe their heritage to the Insular Celts.
There is no modern denomination called "Celtic Christianity", however, and those that lay claim to the title are effectively attempting to reconstruct an extinct flavor of Catholic/Orthodox Christianity that died out when cultural shifts in Ireland and Scotland occurred. This is mainly thanks to English imperialism, as well as power and authority within Western European Christianity being concentrated at Rome, who asserted their dominance over the Mozarabic (Spanish), Frankish, English and Celtic local churches.
Every single country venerates certain Saints who had great relevance to them; for the Irish, one has St. Patrick, St. Columbane of Iona, St. Brigid, among a whole host of other Irish monk-Saints. The same is true for the Scottish as well, though I'm not as familiar with the history of the Scottish church. Likewise, the Germans have their own particular Saints, as do the English, the Italians, the French, the Spanish, the Latin Americans, the Hungarians, the Polish, and so on, and so forth. Any particularities of Celtic Christianity would have been borne out of influences from pre-Christian Celtic culture on the local Celtic Church, but this would not in any way involve a pure mixing of Celtic pagan and Christian beliefs; rather, Christianity would have been expressed through the Celtic culture of the time.