Most common type of printing
Offset printing is the most popular type of printing in today's printing industry. It is true that it has many varieties and uses different techniques and materials (paint, paper). The main division is cold printing, where the paint is fixed by soaking into paper. While the 'hot' offset where the printed paper web passes through the drying tunnel.
The classic offset (water) is associated with the use of water rollers and hydrophilic and hydrophobic surfaces, however, this method is already abandoned due to the difficulty in obtaining a good balance of water and oil paint.
The successor of this method is anhydrous offset printing where silicone molds are used instead of water.
Wikipedia about laser printing
Laser printing is an electrostatic digital printing process. It produces high-quality text and graphics (and moderate-quality photographs) by repeatedly passing a laser beam back and forth over a negatively charged cylinder called a "drum" to define a differentially charged image.1 The drum then selectively collects electrically charged powdered ink (toner), and transfers the image to paper, which is then heated in order to permanently fuse the text, imagery, or both. As with digital photocopiers, laser printers employ a xerographic printing process. However, laser printing differs from analog photocopiers in that the image is produced by the direct scanning of the medium across the printer's photoreceptor. This enables laser printing to copy images more quickly than most photocopiers.
Shortly about solid ink printers
Solid ink printers, also known as phase-change printers, are a type of thermal transfer printer. They use solid sticks of CMYK-coloured ink, similar in consistency to candle wax, which are melted and fed into a piezo crystal operated print-head. The printhead sprays the ink on a rotating, oil coated drum. The paper then passes over the print drum, at which time the image is immediately transferred, or transfixed, to the page. Solid ink printers are most commonly used as colour office printers, and are excellent at printing on transparencies and other non-porous media. Solid ink printers can produce excellent results. Acquisition and operating costs are similar to laser printers. Drawbacks of the technology include high energy consumption and long warm-up times from a cold state. Also, some users complain that the resulting prints are difficult to write on, as the wax tends to repel inks from pens, and are difficult to feed through automatic document feeders, but these traits have been significantly reduced in later models. In addition, this type of printer is only available from one manufacturer, Xerox, manufactured as part of their Xerox Phaser office printer line. Previously, solid ink printers were manufactured by Tektronix, but Tek sold the printing business to Xerox in 2001.