DeskJet is a series of Inkjet printers from HP for home or office (but on a desk) use. They also have OfficeJet, DesignJet, and of course, LaserJet.
Inkjet use a printhead that ejects tiny droplets of ink onto paper to print. Specific technology differs slightly between the Canon implementation (known as "bubblejet") and HP's implementation ("thermal inkjet"), but the result is about the same: ink on paper. The printhead moves, and the paper moves, resulting in images.
Laser printer works similar to a Xerox copier. A laser scans the print drum, deenergizing some sections while leaving other sections alone. The deenergized sections was then passed through a toner area, which then picks up tiny black toner particles (the unenergized areas does NOT attract any toner). The drum is then pushed onto the paper, which pulls the toner away from the drum through opposite charges. Finally, the paper goes through the "fuser", which uses high temperature to "melt" the toner particles onto the paper, fixing them permanently.
There's really no "best", as each inkjet and laser each have their "niche". Inkjets are low cost (as low as $50) and can do color printouts, but are relatively slow. More expensive ones are faster. Lasers are usually much faster but usually only do black, unless you pay for a color laser which still costs over 1000 dollars.
