A light caustic is the result of light reflected from a curved surface.
The attached images show an example of a coffee cup caustic and its geometry. A coffee cup caustic has two main parts:
cusp: Each of the pointed ends of the crescent of a coffee cup
caustic, formed by light rays making smaller angles on a coffee
surface.
fold caustic: The tails of a coffee cup caustic, formed by light
rays making larger angles on a coffee surface.
Another example of a coffee cup caustic appears in J.F. Nye*.
In general, F.J. Wright** observes that a caustic is the envelope
along which geometrical light rays coalesce.
The coffee cup caustic is an example of what is known as photonic catastrophe.
Photonic catastrophe theory comes into play here in the study of
sudden and dramatic shifts in the behavior of reflected light.
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* Nye, J.: Natural Focusing and Fine Structure of Light. Caustics and Dislocations.
Institute of Physics Publishing, Bristol (1999). xii+328 pp., MR1684422
** Wright, F.: Wavefield singularities: a caustic tale of dislocation
and catastrophe. Ph.D. thesis, University of Bristol,
H.H. Wills Physics Laboratory, Bristol, England (1977).
https://researchinformation.bristol.ac.uk/files/34507461/569229.pdf
This topic is new to me. My layman's answer is that the light caustic and the photonic catastrophe are the same. The latter probably more sensitive to incident light angles, but the same. I wanted to read about the catastrophe but the link you gave does not work.
Do you like snorkeling? The ever moving and changing light patterns on coral caused by tiny waves of the sea-surface could be labeled caustic, but just as well catastrophe.