Picture a typical water hazard, say, a creek that crosses the fairway or a pond in front of the green. If a golfer hits into such a water hazard, it's not problem to take a drop behind the spot where his ball entered the hazard.
A lateral water hazard, however, might be a creek that runs alongside a hole, or a lake to the side of a fairway that extends all the way back to the tee or beyond. Dropping behind such a hazard would not just be inconvient, it would be unfair. That's why lateral water hazards are handled differently than "normal" water hazards.
And, by the way, different sections of the same body of water on a golf course can be designated a water hazard and a lateral water hazard. Picture a pond that runs alongside the hole, then fingers out into the fairway. That part crossing the fairway - which can be easily dropped behind - would be marked with yellow stakes and lines; that part alongside the hole would be marked with red stakes and lines.
As for dealing with a ball that has entered a lateral water hazard: Golfers have the same option to play from the hazard if they so desire.
More likely, a golfer will assess himself a 1-stroke penalty and take a drop. The drop can be taken within two club lengths from the point where the ball crossed the margin of the hazard, no nearer the hole. Or a golfer can go to the opposite side of the hazard and drop at a spot on the hazard's margin that is equidistant from the hole.
A ball is considered in the hazard when it lies within the hazard or when any part of it touches the hazard (remember, stakes and lines are themselves part of the hazard).
Rules covering lateral water hazards are covered in Rule 26.
