Instead of looking for "different types of optocouplers" you should rather look up the different types of transistors and other switching devices like the simple bipolar transistor that is in the PC123 and the triac you find in the MOC3051.
What I mean is that an optocoupler is typically just that bog standard transistor/switching semiconductor, but that is switched by a light beam instead of the usual electrical connection, so the generic behavior of that particular device applies.
Also, would be good to see what circuit you had, captures mean nothing when we don't know what you wired and what you were measuring.
The triac (look it up) is typically used to switch AC, and turns off when the AC it switches crosses zero and the control signal is absent. It seems you're talking of a zero crossing of your LED supply which obviously is something else.