This is what I can find out about the alphabet soup from my own manuals plus some googling.
It all begins with ABS
ABS Anti-lock Braking System
Rotational speed sensors on each wheel detect lock-up and release the brakes on that wheel (pulse them, high-speed cadence braking, which is what you feel through the pedal). If either rear wheel locks, both rear brakes are pulsed.
TCS Traction Control System
ASR Anti-Slip Regulation (seems to be Skoda-speak for TCS)
The same wheel sensors are monitored for difference between rear and front wheel speeds. If the fronts appear to be going too fast, the TCS system tells the ECU to reduce engine power.
EDL Electronic Differential Lock
VAG seem to combine this with TCS/ASR. It mimics the effect of a limited-slip differential by sensing any difference in the rotational speed of the two front wheels and braking the faster wheel using the ABS system. Power is cut back at the same time.
EBC Engine Braking Control
MSR Motor Speed Regulation
This is the equivalent to ABS but applied to engine braking: if excessive engine braking on a slippery surface starts to lock the front wheels, some power is applied to reduce the engine braking. Not seen on Seat's as far as I know, seems to be found on some Skoda's and VW's
ESP Electronic Stabilization Program
This system uses extra sensors which measure the steering angle, yaw rate and sideways acceleration and modulate both engine power and wheel braking to stop the car spinning, keep it pointing more or less where the steering input says it should go.
So, ABS and EDL use the brakes via the ABS pump, which you should notice. That leaves TCS, unless you have ESP? The TCS fault is most likely to be in one of the wheel sensors, which can get dirty, or be knocked when changing pads or disks, dislodging or disconnecting them. A VAG-com scan should detect a wheel sensor issue. If not the sensors, then a dealer would recommend changing the ABS unit, where the TCS software sits. I think they're expensive.