The lasers can be classified by various ways, as explained below:
a) State of laser medium: According to state of laser medium, we have solid state lasers like ruby laser, gas lasers like helium-neon laser.
b) Mechanism of pumping: According to pumping mechanism, we have flash light or optical pumping based lasers like ruby laser, electric discharge based laser like He-Ne laser.
c) Nature of output: According to nature of output, we have pulsed lasers like ruby laser and continuous wave lasers like he-Ne laser.
d) Wavelength of output: According to wavelength of lasers, we have ultra violet, visible and infrared lasers.
Reference: This article is referred from my authored book “optics and lasers” having ISBN 81-272-2948-2. In case of any doubt, post in the comment section.