> I realized that these circuits coincided with breakers on the right side of the box. From this, I found out what is apparently a common pattern: we have two 120V out-of-phase incoming lines together with a grounded neutral that is presumably the center tap on the secondary winding of the local transformer.
That's exactly right... this sort of split phase approach is common, at least in the US. Larger consumers can have 240V available to them and everything else is 120V. (Larger consumers can mean things like ovens, ranges, wall AC's, normal AC's, larger shop tools... the list goes on and on.)
Split-phase also has a couple interesting failure modes. A few years ago, we had a case where a 120V heater would cause fans in other parts of the house to speed up when it switched on. What was happening was that the neutral wasn't fully grounded, so when the heater switched on one phase, it pulled the neutral's voltage in a way that caused the other phase's voltage to go up. Once the electrician figured that one out, it was fixed with the quickness. (Not safe or good for electronics at all.)