A zero crossing SSR only turns on or off when the AC wave is at zero volts. A non-zero crossing SSR can turn on
at any point, but again can only turn off when the AC is at zero volts.
If you're trying to dim a light or speed control a universal motor then you need the non-zero crossing type. If you're controlling a heating element then it's really not necessary; you can get enough granularity switching the element on/off 120 times/sec. It depends on the application.
Probably worth mentioning that you just need a triac and an optocoupler to replicate an SSR. Here's an example of an AC dimmer project
. I'm sure you can find many more out there.