Realtime

Realtimerendering is simply what you see while you are producing your image. That means everything that is calculated in an instance (for example >50ms). A 3d-game has a realtime-rendering-application in it.
The disadvantage is easily to understand: The images will not look that good as if the computer had much more time to create and refine them, even so modern graphiccards are very powerful and the images become better and better.
Wireframe, Shaded-View and combinations of the both are used to create the 3d-content in 3d-programs. In the image you can see a wireframe-image.

Raytracing

Raytracing is a quite fast but very powerful, non-realtime renderingmethode. There will be real reflections, speculars and some other things.

The most important characteristic are the hard shadows because light-rays will not be reflected but absorbt by surfaces.

Ambient Occlusion (AO)

To solve the problem of hard shadows without very long renderingtimes there are several different approaches. For example a lightdome, which defines many lights which are placed spherically.

Another way to archieve this effect is Ambient Occlusion (AO). AO adds a default-lightening to the scene. A fast algorithm (which only uses whole areas, not only one ray) will calculate where to add how much of the default-value.

It is very well suited to render productdesigns but it is not very useful for art or very ambient atmosphere.

Global Illumination (GI)

This is a algorithm which can create results which are very much like the once from radiosity but the renderingtimes are a little less.

It will emulate hundreds of lightsources which will be a bit faster than to calculate the reflection of photons from all surfaces.

Radiosity

Radiosity needs very long to render and is not suited very well for animations with that, but it can produce very nice images.

The photons (used from photon-based algorithms like A:M is using them) will partly be reflected and partly be absorbte by every object in the scene.
That is more or less like the reality is working and so you will get very realstic soft-shadows and lightening-situations.

On the image you can see on the one site a wrong setted photoncount-value and on the other site a better setting to explain the algorithm.

Caustics

Caustics are the reflections on the ground on a pool or from any transparent object on another object. It is most often used with Radiosity-Calculation and needs very long rendertimes.

Als Caustics bezeichnet man die Spiegelungen von transparenten Objekten auf anderen Oberflächen. Auf gut deutsch: Die Lichtspiegelungen auf dem Grund eines Swimmingpools oder die Lichtspiegelung eines Glases, dass von der Sonne beschienen wird.

Sub Surface Scattering (SSS)

All surfaces will absorb and reflect a part of the light. But the light will not stop at the surface but may penetrate to deeper surface-layers.
Most surface are will not let the photons very deep in, so it is not very noticeable for us, but there are some exceptions: The human skin or wax for example.
The photons will penetrate the first skinlayer and go deeper in your skin till they fade away.

The skin will look like it would glow from inside and this effect is called SubSurfaceScattering.