Different between Inductor types?
The most important property of an inductor used in an inverter circuit is the current allowed to run through it. A tiny axial inductor may have the same inductance as a radial one but most likely it has a much smaller maximum current.

The inductance needed depends on the voltage spread you want to achieve.

I recommend to stick to the datasheet of the regulator chip closely. They usually give figures which inductors you should use for which voltage and current.