There are 4 main types of printers used today each with there own reason for been on the market, They all print onto paper though with different methods some old some new.
Ink Jet and Bubble Jet
These types of printers are the most popular when it comes to non-commercial use. They work by spraying ink onto the page to form a reasonably high quality and fast print out, Though they can very easily smudge if not left to dry for a few minutes.
Laser Printers are slightly more expensive than Ink Jet printers though can create very high quality print outs. They work similar to a photocopier. First a roller is charged with electricity, a laser is then used to remove the charge in sections, The parts of the roller were there are no charge (where the laser hit) attracts powdered ink and is then transferred to the paper.
Dot matrix aren't the most amazing printers. They simply use multiple small pins which when told to do so indent the paper and leave a small blob of ink. This produces are very low quality print. Though they do have the uses, for example large business use them for printing invoices as the machines are cheap to buy and run.
Dye Diffusion Thermal Transfer
Dye Diffusion Thermal transfer is also known as Thermal Dye Sublimation, Dye Sub and Thermal dye Transfer is a process used by colour printers. The process begin by a crayon like wax film is moved across the page, The pigment is then heated onto the paper. One of the main differences between this type of printer compared to others available is that the paper usually goes through the printer 4 times (one for each colour).