Thanks for the Q and the comments!
The ones with the Ignitors would be used mainly with High Pressure Sodium lamps [the ones that produce orange/pink orange colored light, or the ANSI category "S" lamps - e.g. S51].
Some Metal Halide lamps use an Ignitor with the Ballast, mainly for a faster restrike [restart after a momentary power interruption, or even low enough dips in voltage]. Metal Halide lamps have the blue/silvery blue light output, larger and fatter arc tubes - as compared to the thin, long arc tubes of a Mercury vapor lamp. Their ANSI category is "M" [e.g. M57].
Metal Halide lamps might take upto 15 minutes to restrike, so the Ignitor being included here would bring the restrike time upto 3-4 minutes.
There are also a few medium base M lamps that do not include the typical starting electrodes within the lamp that normal M and H [Mercury Vapor] lamps do. These would need the Ignitor for both cold starts and restrikes.
For S lamps [High Pressure Sodium], they all require high voltage pulses from the Ignitor for both cold starts and restrikes. Without the Ignitor, the lamp cannot establish an arc between the lamp's electrodes [AKA across the arc tube], only minimal levels of current will flow through the arc tube.
BTW: The term "Arc Tube" is in reference to the tube inside of an HID lamp's envelope, where the production of light is done.
The arc tube contains Mercury, plus some inert substance [such as Sodium "Na"], and is a separate entity from the outer glass envelope.
The envelope is the outer part of the lamp, and the only part you can readily touch [unless you break it... then you can touch the arc tube
All the envelope does is protect the arc tube [and double result it protects the surrounding enviroments from the hot arc tube - with hot meaning HOT!!! Very much red hot!], plus it acts as an UV filter. Some lamps incorporate color correction into the envelope.
Let me know if this covered your Q, or just opened the door to the Twilight Zone