J1772 on the Zero S is a bit confusing, because the standard is usually associated with both 240V charging and faster charges than are available from a standard 120V / 15A wall socket.
With the adapter installed, the Zero S should be compatible with J1772. (2011 only? Don't see the option for the 2012 bikes). The onboard charger is limited to 1kW output power, so at 240V the Zero S should pull around 5A.
It seems the SAE
defines AC Level 1 charging as 120V <16A and AC Level 2 charging as 240V <80A. That would mean the J1772 Zero and any EV bike charging from a Euro-style 240V mains are all considered level 2 bikes.. even if they're charging at rates significantly below what a 120V / 15A socket supports.
Zero's quick charge option is completely separate from its J1772 option. Quick-charging uses multiple off-board chargers in conjunction with the onboard charger to deliver total power to the bike of up to 4 kW (4 120V circuits at approx 10A each). The J1772 option is a 240V interface to the single onboard charger, delivering total power of up to 1 kW (1 240V circuit at approx 5A).