I've never heard or seen helical staircase. Apparently my confusion is common, as this page explains: http://thestaircaseexperts.wordpress.com/2013...
"Spiral staircases have circular stairwells. The steps wind around a newel (or the central pole) to support the steps, with the handrails on the outer side of the circle, while the inner side of the staircase contains the central pole."
"Helical staircases differ from spiral staircases as they do not have a newel, and handrails are present on both sides. They are also not limited to a circular staircase, and may be built in an elliptical or oval shape."
I'm not an architect, but it looks to me as if the German Wendeltreppe can be either a helical or spiral staircase, depending on the architectural features. If the Wendeltreppe is actually a Spindeltreppe, then for AE spiral stairs or spiral staircase would be both more correct and commonly used. In a very general text, helical staircase might seem out of place. I don't think it is commonly used or known by lay people.