Rusty, it's fascinating!
I have looked them both up.
"Hair ice" as you say, forms on dead wood and takes the shape of silky, fine hair
Only this last year, scientists identified the fungus that is responsible for the formation.
Yes, you are right, a frost flower is something different.....in freezing conditions, the sap in the stem of plants expand, and when cracks form, water is drawn through them, which then freezes on contact with the air. As more water is drawn through, the thin ice layers are pushed further back, causing a thin "petal" to form.
Both are incredible feats of nature, aren't they?
As Malone said, there are some terrific pictures of both instances!