Global Illumination alternatives

The thing is that, I just can’t understand what AO and indirect shadowing have in common besides the fact that AO makes a fake CONTACT shadow (although, it’s still an indirect shadow, yes).
AFAIK, AO can’t provide actual shadows, it just fakes them. And one more question: how can imperfect shadow (ISM) maps be static?

Yet again, any criticism is welcomed, of course I might be wrong about that (I know not that much of AO, but I really think ISM are dynamic).