Which method of rapid prototyping or 3D printing is the fastest? This is a great question to take into consideration when thinking about purchasing a 3D printer. I'll answer this question in reverse order from the slowest to the fastest methods.
This method isn't 3D printing, but I wanted to mention it. Machining is a traditional form of manufacturing which has the power to do some pretty cool stuff, but it doesn't hold up against the speed of 3D printing. This applies to all forms of manufacturing, but the speed depends heavily on the design and material that you are creating something with. Traditionally, machining takes hours on top of hours, days, and sometimes weeks to manufacture parts. Yet again, this depends on the design, but if you were to order a part from a machine shop it would likely take a week or longer.
The slowest form of 3D printing would be Fused Deposition Modeling, or FDM technologies. This is a CAM system that involves the melting of material from a string on a spool. A nozzle will draw on a string of material from a spool, and the material will be melted by the heat off of the nozzle. Think of a hot glue gun as a similar analogy. Material (or glue) will be shot out of the hot nozzle (the nozzle on the hot glue gun) and melted on to a build table. The layers of melted material will be stacked up until the final product is completed. This form of manufacturing is very quick, as products can be created within a matter of hours, it just isn't as fast as other methods.
A quicker method of 3D printing that I will talk about is DMLS, or Direct Metal laser Sintering. This process consists of a 3D printer laying down layers of metal in powdered form. As one layer of metal is laid down, the printer will melt it together in accordance to the design with a laser. Another layer is laid down, and the process repeats until the final product emerges. One could argue that this method of 3D printing is faster than inkjet printing, but I am ordering DMLS as 3rd place, as many manufacturing processes involve the melting of other metal alloys to be used in conjunction. For example, after a print is made of stainless steel, sometimes bronze alloy powder will be placed around the product, put in a box of some kind, and placed in a furnace so that the bronze will melt into the stainless steel. This melting process takes a few hours on top of the original print which also takes a few hours.
Ink jet 3D printing is very fast, and at the same time very similar to DMLS. Layers of powder are laid down just like they are in DMLS methods, except the powders aren't fused together by lasers. Rather, they are held together by an adhesive chemical. The final product is removed from the 3D printing machine, and the excess powder is brushed off in preparation for infiltration. The product is usually very weak, and filled with around 40% air. A super glue like chemical or epoxy is dripped over the product, where it will then form inside of the product to strengthen it. This post-preparation leaves this method behind traditional SLS methods.
SLS, or selective laser sintering is very similar to DMLS. In fact, it is practically the exact same kind of 3D printing. The only difference would be that there is virtually no post-preparation for the product, it is taken from the printer and ready to go!
The fastest form of 3D printing is Stereolithography, or SLA 3D Printing. This method involves an ultraviolet beam of light hitting resins that are sensitive, which solidify. This process moves incredibly quick, and results in a product (depending on the design) being prepared in a couple hours.