A red dot sight uses a reflective surface on the front of the lens to bounce the light back at you, creating a "false image" of the dot or reticle. What you are aiming at cannot see the dot... it can only be seen looking through the reticle. The most common red-dot scopes use red light, although not all of them are such.
A laser actually pushes a beam of electron radiation amplified light forward. This light bounces off of the aim point and returns to your eye. The most common lasers are cheap and red in color.
Advantages of Red Dot:
unlimited range, paralax corrected sights to decrease paralax at short range, fast target aquisition, cheaper than holographic sights, can use zoom lenses to extend effective range, legal to hunt with in many states, can fire with both eyes open, can be used on a shotgun to shoot skeet
Disadvantages of Red Dot:
High battery consumption on highest powers, bright light can cause issues seeing the dot in the reticle if you don't use a tube and shaded red dot, unless you spend a lot, the dot is 5 MOA at 100 yards (decreases accuracy), cheap red dots can break from high powered kicks, reticle can get dirty or cracked easier, not useable as a hand guard unit on pistols, not useable on the bottom rail of a pistol, few flashlight/red dot compact combos that are one piece..
Advantages of Lasers:
Fastest target aquisition on the market, head does not need to be canted behind the bolt (no chance of getting hit by the action or the scope), can fire with both eyes open, no reticle to clean, hand guard options for pistols, bottom rail option for pistols, often combod with flashlights to reduce space/weight/and reduce chance of damage by bumping.
Disadvantages of Lasers:
VERY limited range, cheap lasers can only be seen at 30 feet in daylight, high cost for quality lasers, high battery consumption for powerful lasers, illegal to hunt with in many states for various prey, if mounted on top rail, makes it almost impossible to shoot skeet with a shotgun (size dependent), no option to add magnifiers to extend range (light diffusion limited on distance)