Pico doesn't have grounded tip, but you can hack it
Yes, Nano has exactly the same PCBs inside the station and soldering iron. The difference is different heating element and no ground wire from mains wire to the main PCB. Also could be non ESD safe plastic for the case and soldering iron, but that needs to be tested. On the other hand, it's not said that OP has grounded outlets in his home in the first place.