In my opinion, it's both ABV and ingredients. To me, hard cider says only cider, fermented. No sugar or other stuff added, and a lower ABV.
When I hear "wine", I think of an ABV of 12-15% or so and expect a more complex flavor with maybe some tannin, acid blend, etc, and I also expect clarity. I don't expect a cider to be clear necessarily.
These aren't the definitions of course- just my thinking!
I don't think it makes a difference. I believe the US is the only (?) place that uses "cider" to mean "unfiltered apple juice" and makes a distinction between that and "hard cider". Originally, and in most (?) other countries, "cider" is what you get from fermenting apple juice (filtered or unfiltered) - there is no distinction between "cider" and "hard cider".