They both do the same thing, functionally speaking. But I prefer the first pic with the ignitor built into the ballast, because this frees up a lot of space behind the projector. Most cars where you are retroing projectors into have limited space to mount anyways, so if you have a huge ignitor module mounted on there too, then you just lost another 1-2 inches of mounting depth. I say go with the first pic you supplied if your space is limit directly behind bulb, but if you got tons of space and you have no space nearby to mount the ballast then go with the second pic you supplied, because you can extend the ballast to ignitor wires from the trunk to the bulb if needed (if you have no room to mount near bulb. The first pic you showed only allows you to mount ballast within like 12 inches of bulb. Hopefully this helps you understand better
i got confused when received offer for those two types of ballasts.