Yes, there are four primary taps on the transformer. This is to vary the voltage (and thus the current) to the secondary which allows for different power output for small and large tips. Too much power on a small tip will turn it cherry red in a second and burn it up (already burned on up myself).

 

Can you think of a reason only using the zero point would benefit this system and the heating process? The voltage being at zero throughout the cycle...

 

There is very little difference between the SSR and relay switching except you do not get contact failure etc, with zero cross there is no really big advantage except cleaner switching.
The voltage on the primary is identical both ways.
There are other types that give you options you cannot achieve with relays, such as phase angle control, but that is not used here.
Max.