There are three different types of 3D printers:
FDM = Fused Deposition Modeling
DLP = Digital Light Processing
SLA = Stereo-lithography Apparatus
In this primer, we concentrate mostly on FDM style printers. The supplies are much cheaper and the printers can create larger and more robust prints. FDM printers use rolls of plastic filament and what looks like an automated glue gun (hot end) to lay down layers of plastic and build up the item being printed.
DLP and SLA printers use a liquid photosensitive resin and a UV light light source to form the item. The big advantage of SLA printers is their ability to print fine detail. The disadvantage is a limited number of resin options and additional work post printing to fully harden the item.
If you already have a number of FDM printers, adding a DLP/SLA printer to support small prints with fine detail might be worth considering. For your first printer, FDM is odds-on the way to go.
This video goes into detail on the differences in printing, post processing, safety and supplies for the three printer types.