Citizen Printer

What category type of printer is a dot matrix?

Also, what category of printer is an ink-jet?

i'm not sure what you mean by "category" but a dot matrix printer is a little outdated. it uses an ink ribbon like an adding machine or typewriter. a laser printer uses a toner cartridge and is capable of much more detail as well as much more speed in printing. a dot matrix printer is OK for text but with the advent of computer graphics, the laser printer was a necessary step forward.
What categories are there to choose from? I am only aware of a few different types of printers: laser, inkjet, offset, and dot matrix. A dot matrix printer is of the dot matrix type. Same with inkjet. Please clear up the question.
Dot Matrix - I would think impact. Inkjet is ink jet.