Don wrote:

....
Spiral stairs have a center structural member that supports one side of the
treads.
Helix stairs have no center support and rely on the structural integrity of
double stringers on either ends of the tread. Notice that the helix stair
will have 2 diameters, one to inside stringer the 2nd to the outside
stringer. Spiral stairs have only 1 diameter.
http://www.spiralstairsofamerica.com/gallery.html

What's being argued here is geometric definition as opposed to common
usage...

The geometric definition of a helix is the straight line drawn on the
surface of a cylinder. The Oxford dictionary lists the first definition
(common usage) as "spiral". From a geometrical viewpoint, the rail of
what you defined as a spiral stair is, in fact, a helix.