There are said to be 5 types of helicoids.
The pictures in the links are hard to tell apart.
Scripting their parametric equations may help to discern the differences.
There are also many links to other, older, papers.
The ASWT may be a conical version of the Oblique helicoid, or of the Developable helicoid. (???)

V. J. Paul, “A review of geometry investigations of helicoids,”
https://www.researchgate.net/publication/325860850_A_Review_of_Geometry_Investigations_of_Helicoids/fulltext/5b29e65faca27209f374d62b/A-Review-of-Geometry-Investigations-of-Helicoids.pdf

Five Types of Ruled Helical Surfaces for Helical Conveyers, Support Anchors and Screws
https://www.matec-conferences.org/articles/matecconf/abs/2017/09/matecconf_icmme2017_06002/matecconf_icmme2017_06002.html

- Brian

Found some nice links to knitting as well.