A trigger coil generates a HV pulse which causes the Xenon Gas to ionize to allow the strobing. I D/L'd one of their Flash head manuals. The flash and burst coils will taylor the discharge rate. Note that they don't show an iron core on the flash but do on the burst coil. The burst coil also has series resistance downstream. Less resistance and inductance will yield a very high current, rapid capacitor discharge and bright flash. The high inductance of the iron core burst coil and series resistor(s) will yield a lower current, longer discharge. Plus, you dissipate some of the power in the series resistance.
Joe