I suppose we all have our own ways of thinking about this. I don't play many ornaments (on banjo/mandolin) but I play in a way that (I hope) fits in with an Irish session.

To me, it is very much the rhythm. I find the way a tune set goes can vary depending on who starts it, from session to session etc. but to me they are all in some Irish session ballpark.

I find English rythms different in feel to the Irish range and I find it harder/less natural to adapt.

Hope that makes some sense - it's difficult to explain how I try to feel it.