ok well i don't know a great deal about the EMS side of things, just that often the input to it is a torque demand.. or demand for a certain reduction in torque.
a few generic variants:
engine only - as described above, retard ignition (etc?) to reduce torque to drven wheels & reduce slip.
brake only - probably not practically used. use the hydraulics usually associated with ESP to brake the driven axle & reduce slip. nasty. but can also operate as below.
brake & engine
- for straight line traction launch usually just demands engine torque reduction
- if the driven axle is on different surfaces (ice patch?) the diff means that wheel will spin up and you go nowhere. in this case the brake is applied to that wheel to allow some drive to go to the one that has some traction.
- what order of precedence these come in probably depends on the system & vehicle tuning.
EBR as defined in mole's post can just be an add on to ABS (i.e. not necessarily full ESP & brake based TC).. as it is aiming for the same purpose - preventing wheel lock under braking. not much point having a superb ABS system if the driver brakes in a low gear and the engine drag is sufficient to lock the wheels. in this case as stated a increase in engine torque is demanded! ... disturbing.. but fortunately only usually required in extreme circumstances (i.e. braking/downshifting in a low gear on ice).
thats my take on it anyway.
not done much tuning of it myself but the ultimate test is usually a split tarmac / polished ice traction hill..... where a bad tune will see you going backwards