Is each brake modulated independently when traction is lost at that wheel? Or does one wheel locking trigger a chatter response at all wheels? Or are there different systems about?

Anything modern the ABS control box limits it just on the slipping wheel Early systems may have triggered all the brakes akin to cadence braking but the fact it only operates on the slipping wheel is why in most cases (barring deep snow or mud where the build up infront of the skidding wheel is benificial) ABS is superior to cadence braking – coupled with the fact its on and off many times a second rather than every few seconds with the cadence braking.

Definitely per wheel on my Fiesta and mrs rocket’s Corsa 🙂

Brake types
Anti-lock braking systems use different schemes depending on the type of brakes in use. They can be differentiated by the number of channels: that is, how many valves that are individually controlled—and the number of speed sensors.[24]

1) Four-channel, four-sensor ABS
There is a speed sensor on all four wheels and a separate valve for all four wheels. With this setup, the controller monitors each wheel individually to make sure it is achieving maximum braking force.
2) Three-channel, four-sensor ABS
There is a speed sensor on all four wheels and a separate valve for each of the front wheels, but only one valve for both of the rear wheels. Older vehicles with four-wheel ABS usually use this type.
3) Three-channel, three-sensor ABS
This scheme, commonly found on pickup trucks with four-wheel ABS, has a speed sensor and a valve for each of the front wheels, with one valve and one sensor for both rear wheels. The speed sensor for the rear wheels is located in the rear axle. This system provides individual control of the front wheels, so they can both achieve maximum braking force. The rear wheels, however, are monitored together; they both have to start to lock up before the ABS will activate on the rear. With this system, it is possible that one of the rear wheels will lock during a stop, reducing brake effectiveness. This system is easy to identify, as there are no individual speed sensors for the rear wheels.
4) Two-channel, four sensor ABS
This system, commonly found on passenger cars from the late ’80s through the mid 1990s, uses a speed sensor at each wheel, with one control valve each for the front and rear wheels as a pair. If the speed sensor detects lock up at any individual wheel, the control module pulses the valve for both wheels on that end of the car.
5) One-channel, one-sensor ABS
This system is commonly found on pickup trucks, SUVs, and vans with rear-wheel ABS. It has one valve, which controls both rear wheels, and one speed sensor, located in the rear axle. This system operates the same as the rear end of a three-channel system. The rear wheels are monitored together and they both have to start to lock up before the ABS kicks in. In this system it is also possible that one of the rear wheels will lock, reducing brake effectiveness. This system is also easy to identify, as there are no individual speed sensors for any of the wheels.