What are the outputs of single-chamber brine electrolysis?

From my googling around, the internet states, with extremely high confidence, two different mutually exclusive sets of outputs for single-chamber electrolysis of salt water. (Well, plus a bunch of stuff about using membranes.) I'm aware of the three common methods of the Chloralkali process, but I'm specifically interested only in the question of what happens if you do it with just... saltwater, nothing else in the water and no membrane or barrier or mercury layer.


Option 1 is that you get H2 at the anode and Cl2 at the cathode, and the water starts getting a concentration of NaOH. The total reaction is 2NaCl + 2H2O -> 2H2 + Cl2 + 2NaOH. This makes perfect sense to me.


Option 2 is that you get O2 and H2 at the cathode and anode respectively (or the other way around, depending on the source!), and the water gets either just a higher salt concentration or a mixture of that and some other stuff like NaOCl.


What actually happens, and why are websites that are claiming to be scientific instruction all disagreeing on something that should be so basic and empirically verifiable?


