I think this might be like other fields, where the more you learn the more you find there is to know.
So people who don't care much about it may think shamrocks and Danny boy sums up Irishness. And no harm in that.
We went to a workshop at a folk festival and learnt Irish Dancing. Then we went to another, at another festival and found that what we were taught was completely different. We now know that the varieties are almost endless, from step dancing of all sorts (not just the 'River Dance' kind), Ceilidh dance, Set dancing (the use of the term meaning dances in sets of 4 couples based on 19th century Quadrilles). And within Set Dancing there are different styles of footwork the figures are done in different ways depending on where and when the dance was collected.