They are the same thing. Both use an optical sensor (basically a simple camera sensor with an extreme close-up lens) tracks the motion of imperfections on your table or mouse pad to determine which direction and how fast the mouse is being moved.
A laser mouse uses a visible laser LED to light up the surface so the optical sensor can see it. The laser is typically in a visible wavelength, not because it has to be, but because most cheap laser LEDs are designed for other applications in those wavelengths (barcode scanners, CD/DVD/Blu-ray readers, etc).
An optical mouse uses a LED that's invisible to the eye, usually infrared (commonly used in remote controls). The optical sensor can see infrared, so it works just like the laser light at lighting up the surface. There's an argument that IR allows it to track on more surfaces. In my experience it's generally true, but sometimes the opposite is true. e.g. The optical mice I've used have trouble tracking on cardboard, which never gave laser mice problems.
The precision of either depends more on the camera optics, not the light source. That said, the recent trend has been towards optical mice (someone decided not being able to see the light source was better). So the mice using IR LED emitters tend to be newer, and have better camera sensors, and track better than the older tech laser mice.