I find these linguistic differences interesting enough. Perhaps I should have said in English speaking countries this side of the water, but it would have sounded a bit redundant, since the the remark was about a difference in terminology between English-speaking countries anyway.

I'm not aware of ever having heard people here refer to the ice version as anything but Ice Hockey, or the field version as anything but Hockey. I've always assumed the field version came first, a tamed down version of Hurling, and that people in America shortened "Ice Hockey" to "Hockey" because maybe it's a more common game than the field version. But maybe it's the other way round.