Yes, I was referring to the overcurrent condition as being the fault, the condition they are protecting against.
There are various different well defined characteristics, how much time needs to elapse before the MCB trips:
A Comparison of Thermal and Magnetic Tripping Characteristics of MCBs
info.e-t-a.com
Just looking at RS, I see MCBs from 160mA, with there being typically 500mA intervals once you get into the few amps range. They even stock a 5kA option, which is I imagine aimed at datacentres or something like that.
The mechanism is a sensing circuit in parallel to the mechanical switch, so basically the current sense is out of circuit, much like how a multimeter measures current without affecting it's flow through the circuit. The characteristic curve is then calculated from this current flow measurement, so it can, say, trip if an overcurrent of 2x is detected for so many seconds, so you can avoid tripping on inrush current and that sort of thing.
I can see benefits if you are of the persuasion that anything in the way of current is a bad thing. Much more plausible than polishing your fuses