Is there a set point when wide becomes ultra wide?

[neuroanatomist]

Typically (FF equivalent):

Wider than 24mm = ultrawide angle
24mm - 35mm = wide angle
36mm - ~60mm = normal
~60mm - 100mm = short telephoto
100mm - 300mm = telephoto
Longer than 300mm = super telephoto

Technically, 24mm on APS-C isn't even wide angle, it's normal (which is why I don't usually recommend 24-xx zooms as walkaround lenses for crop bodies).

[Black_Dog]

I have always thought of ultra wide-angle lenses threshold as the point where distortion becomes really noticeable, which is about 24mm on a 35mm film camera. I recently learned there is a technical reason for that.

An ultra-wide angle lens is one whose focal length exceeds the short dimension of the film or digital sensor.

A 35mm film negative or full frame sensor measures 36mm x 24mm, so anything wider than 24mm is considered ultra wide-angle for that format. Likewise, Canon's APS-C sensors measure 22.3mm x 14.9mm, so anything wider than about 15mm is ultra wide-angle.