Let's start (In a more or less chronological order):
FDMThe first method of three-dimensional printing was the Fused deposition modeling. It was invented in the eighties. FDM is the "traditional" way of rapid prototyping. The way it works isn't very complicated:
There is a so called extruder, which is about 200 - 300 °C warm (depending on the printed material). In the middle of the extruder is a hole, where the plastic (for example ABS, PLA, PVC, etc) is melted. In the most of the "fabbers", the extruder is fixed, and the (mostly warmed) printing-bed is moved.
The model is fabricated layer by layer with this procedure (like in every other technology I'm going to talk about :D).
SLMThe Selective Laser Melting is another way to "print" models. Not these but these models. It works like that: We have a bed of powder (f. e. Polyamide (especially Pa-12)) and a high-energy laser (up to 30W). With our laser it's easy to melt the powder and get a stable shape of "plastic". It's also possible to do this with metal-powder (with a few small adjustments).
SLSThe Selective Laser Sintering is basically the same as the SLM. The big difference between these two methods of printing is the material which is used to print. Also, the density of the product produced with the SLS-technology is lower than the one achieved by SLM. For more information, have a look at this paper or come back to this blog later (there will be more information soon).
LOMLaminated Object Modelling is in my opinion the most intuitive way to print sculptures. The name of the method already tells you how it works: We take a foil of paper (or something else, like ceramic, plastic and even aluminium is possible) and cut out the cross section of our model (the most used cutting-technique is a laser). Now we start doing this again and again and after some time we have our finished model. There are several ways to glue the layers together like polymerisation, galvanic ways or the simplest of all: glue.
SLAThe method which is called "Stereolithography" was patented in 1986 and is another potent type of 3D-printing. Again, we create partially hard plastic. But instead of melting powder we solidify a liquid respectively a kind of a resin. The liquid is a so called photopolymer, a material which changes its properties when exposed to light.
3DP3DP stands for 3 dimensional printing, where a more or less normal printer is used to bind powder. The inkjet like printer does not emit ink but a binding material for the powder. The interesting part about this way of printing is the ability of building full-coloured models.
Of course there are more methods of additive manufacturing, but it would be too much to present all of these techniques. The ones I tried to give a small overview are the most important ones and the current industry standard.