FDM printers squeeze out molten plastomers, like chocolate or ABS and PLA plastic, through a small jet (or nozzle), these strings of plastic are smudged down onto a build surface creating the shapes layer by layer in relatively good detail.
Laser SLA printers use a pin-point focused Laser source, moved by way of motors in fine increments. Displaying pulses of UV light in small areas, to cure pockets of Photo-sensitive resins together to build up layers, in order to create intricate, highly detail parts.
DLP-SLA printers make use of DLP home theatre projectors to display panes of UV light over large surface areas, to cure entire layers of Photo-sensitive resins into intricate incredibly detailed parts.
LED-SLA printers are much like DLP-Bottom-up printers, in that their light source is displayed from beneath a window, over the entire surface area of the layer in one burst.
SLS printers make use of a high powered laser source to sinter together fine powders distributed in perfectly flat, micron thick layers, into large, exceptionally highly detailed parts. These machines usually sinter metal powders, and are primarily used for prototype machinery directly off of the print bed.
With-in SLA type printer builds, there are two more categories that sub divide them.
Bottom-Up printers display a UV light source from beneath an optically clear window into the vat of resin.
Top-Down printers display a UV light source from above, down into the vat of resin.