Yes, it means it doesn't have zero-crossing detection. The latter is useful for purely resistive loads, where the current is in phase with the voltage. For reactive loads, inductive or capacitive, this doesn't offer an advantage.
"Random" just means the triac switches on at the time you signal it to switch on, whatever the voltage phase at that moment. So its actual meaning is that it can switch on at any time.
A note I made earlier on zero-crossing switching:
You may have noticed that incandescent bulbs always fail when they're switched on. That's because the mains phase can be near its maximum when switching on. Combined with the low resistance of a cold bulb this results in a high current peak, which may burn the filament. When you switch on a zero crossing you avoid these peaks.
Random switching is needed if you want to build a triac-controlled dimmer, where you want control of the phase angle where you ignite the triac over the full 180° of a half cycle.
You cannot smoothly dim a normal incandescent light bulb with zero-crossing control of normal 50/60Hz single-phase mains- the filament (even a really fat high-power one) will visibly flicker to an objectionable degree with even a small number of possible levels of control. Similarly, radiant heating is problematic with zero-crossing control because the temperature can change significant within a small number of cycles. In those cases, phase control is typically used.
Normally for zero crossing control we would like a cycle length of several seconds or more (up to maybe 30-60s), so that the number of half-cycles is at least in the low hundreds. That limits the applications to those where the low-pass filter formed by the heat capacity of the various elements will smooth out the power, so generally those applications with a time constant in the 1minute + range.
Phase control has problems that zero-crossing switching does not have (more EMI, there may filtering required for EMC compliance, undesirable audible noise from lamp filaments, nonlinear response power-vs-trigger angle). On the other hand, zero crossing switching of high current loads can cause visible light flickering (otherwise independent lights that happen to be powered from the same mains circuit).
For phase control or for zero crossing switching you need zero crossing detection. In the case of zero crossing switching, the micro can delegate that job to the triac driver and just tell it roughly when it wants the triac on or off, and the driver and triac will respond with some latency depending on when the zero crossing happens to hit.
There's a third alternative- the simplest- random switching, where the triac just switches on whenever it is asked to (and switches off at the zero crossing, since that's all it can do).
If you implement a zero-crossing detector for a micro and drive the triac with a non-zero-crossing opto (or use a random switching SSR) then you can select any of the three options with firmware.
Best Answer
Your application here uses PWM as the output from a PID library routine, I gather. If possible, your PWM period (inverse of frequency, of course) should be the same as the temperature sampling period.
Your sampling period should be as rock-solid repeatable as you can make it; with shorter sampling times being usually better, too. However, variability in temperature sampling translates immediately into poorer performance of the PID, so keep the repeatable nature of the sampling time to below about (in my book) 1:1000 or 0.1%, if possible. This means that if you sample temperature once per second, you want to make sure that you do so down to less than 1 millisecond of variation between samples and, hopefully, as close to zero drift over time as possible, too.
Only when your thermal mass is extremely small and your process is very fast should you consider using phase-angle firing -- because you have little choice about it, then. So in this case, with \$50\:\text{Hz}\$ mains AC say, you should be sampling temperature perhaps at \$100\:\text{Hz}\$ (once per half-cycle.) You'd then apply phase-angle firing and operate your PWM period to match your half-cycle temperature sampling period (also \$100\:\text{Hz}\$ with the PWM duty cycle determining the firing angle where "100%" would mean an immediate trigger going to the MOC3023 [which doesn't have a zero-cross circuit in it] and where "0%" would mean no trigger during that half-cycle.)
For slower thermal mass, which is far more likely I suspect, the PWM period can and should be much longer. Here, you absolutely do want to avoid phase-angle firing to avoid nasty levels of system noise. Here, you will want zero-cross firing that you get with the MOC3063, instead.
For zero-cross firing, the duty-cycle value technically should be an integer multiple of your AC half-cycle period. However, in your case using a library, you may not have any control over that. Instead, the PWM duty cycle duration may be near, but not exactly at, two different integer multiples of the AC half-cycles. This can be a problem, depending on how closely you need to control the temperature and how you set up your PID control parameters.
You could consider improving this integer multiple problem by applying a digital differential analysis, used to adjust each successive actual duty cycle such that the overall average over some successive grouping of them yields the PWM duty cycle average you want to achieve. This helps avoid degrading long-term precision. But I don't know if your library supports this. So that's just another issue to consider, but not necessarily a solution you can implement here.
You have specified very little about exactly what you are trying to achieve. I don't even know the frequency of your mains supply, for example, because you haven't said anything about it. Nor have you specified anything about your thermal mass or, really, anything much else. So this is all that I can offer.