Laser Mouse vs Optical Mouse
The technology used in both laser and optical mice are very similar. The sensors are the very same for laser and optical, basically: a laser mouse is just an optical mouse but the light that is emitted and then received are more concentrated than the regular LED light. The necessary components include a light emitter and a light detector. The distinction, then, is simple: Laser mice use laser as the light emitter whereas optical mice use LED lights.
Invisible light sources in laser or optical mice have the advantage of not hurting the users' eyes in dark environments. The only disadvantage is that it is impossible to tell with the human eye whether a mouse is powered or not just by looking at the light source. Therefore, some mice that use invisible light come with LED indicators to show whether or not the mouse is powered on.
Originally, optical mice used red light as their tracking method. Recently, optical mice started utilizing light within the non-visible spectrum, whereas laser mice have always used invisible lasers.
"Besides their tracking speeds, laser mice work on nearly every surface, whereas optical mice may experience trouble tracking on black or shiny surfaces." 
Some laser mice have problems on some tissues, where the optical works better.
Laser mice allow for higher DPI (dots-per-inch) than Optical mice. DPI is what allows for precise scanning of mouse movement.
Laser mice typically operate at 2000 DPI while Optical mice generally operate at 400-800 DPI.
Normal mouse function can be achieved even with the low-end of the DPI spectrum (400 DPI). Only professional gamers or computer artists will be able to benefit from the extreme sensitivities provided by laser mouse tracking.
For more information on DPI check out Wikipedia's article on the topic.