Shengen visas I believe are just that - any shengen country to another - the original visa remains valid. IF you have a shengen visa. If not, you are down to the entry rules for that country depending on your nationality so its about checking each country individually. I am unaware of any differentiation between arriving GA or scheduled carrier anywhere other than the USA though.
Shengen VISAs are actually about being allowed to enter the Shengen area in the first place, being then able to freely move around within the member countries is an added bonus (actually, that's the point of the whole Shengen thingamagig
).
You can no longer obtain a VISA for a single member country as that would be pointless, seeing as there would be nothing keeping you from then moving around the area freely. Countries that wish to maintain full control over their own immigration policies, like the UK for example, will have to remain outside the Shengen area for that to be at all possible.
Long-term VISAS and work/student permits are another matter entirely, as they give you the right to either reside permanently, work and/or study in a specific member country, therefore local rules will apply. But if you do get issued a work/study or permanent resident VISA in a Shengen member country you will still get a Shengen VISA, meaning you will be able to travel freely withing the area but will only have the right to work/study/reside permanently in the country that issued the VISA. Moving to another country within the area will require you to apply again in that country, as opposed to a full citizen of a member country who will have no restrictions at all as to the purpose and length of his stay.
It's really not as complex as it may seem at first glance once you understand the basic principles, but that Wikipedia page is really pretty awful and makes it look like a true nightmare.
Ciao,
Dg800