Being a willing target is a subset of the targets. You can enter that set in two ways 1) be voluntarily entering it or 2) by being unconscious. If you are part of that set then you don't get a save against any spell.
If you are conscious then you get to make your choice whether to be part of the willing targets set whenever you want (and people can be assumed to default to being unwilling), if you are unconscious then you automatically become a willing target.
Willing is not something that only exists for specific spells, specific spells just restrict you to only willing targets.
The two sections don't reference each other. Willing might be something that only exists for specific spells if you look at the RAW. For other spells, it's "voluntarily forgo[ing] a saving throw". Does common sense tell us it's the same? Maybe, maybe not.
I'm going to go ahead and support015: Unconscious does not mean Mindraped until further notice.