But it isn't.... The coil is in series with the [ STOP button] contacts and the supply voltage...
When they say "in parallel with other tripping functions" they mean that typically a small breaker has (3) ways of
automatically tripping open: Trip Unit [1. Long Delay: sustained overload, like 300% rating 2. Instantaneous: short circuit, like >1000% rating] Shunt Trip, solenoid energized by an external voltage source. On large power breakers, LV, MV & HV class, other trip unit functions exist such as Short Time, Ground Fault, Isq T, etc for system coordination.
"Tripping" is usually referred to as the automatic opening as apposed to the manually opening by operating the breaker handle to off.