First off, screen space ambient occlusion is not a physically based effect at all, so there is no realism argument. Theory of the effect basically states that
any surface that is not covered (optionally within a certain distance) is lit
Even if raytraced it's just a quick and dirty way to bring out small details on models.
Second, all of the techniques in question are just iterations of the SSAO; all of them work as a post process, after the scene has been rendered. This means that shaders have to do something magical to produce anything accurate from little information that remains after rasterization.
This is the oldest technique. It assumes that any pixel within a given screen space radius is a possible occluder. This is roughly approximated by calculating difference of blurred and original Z (depth) buffer and darkening result if blurry version has a greater value.
The pitfall of this approach is that it both falsely darkens and fails to detect certain features. You'll have to take a really good look at this pillar but you'll notice that while the ceiling is falsely shadowed on the sides it is not affected at the junction.
This paper has some more graphic examples.
This algorithm attempts to solve problems of SSAO. It does so by using more information, namely the normal map. Instead of searching for occluders around a pixel in screen space it tries to restore small bits of the scene and make a more informed approximation of brightness that should be there.
You can notice that ceiling much clearly faces down, also, the pillar is darker at the top.
A paper by NVIDIA has some more details on it.
HBAO is a more recent algorithm, it produces much closer approximations of... an approximation.
Images are snippets of these screenshots.