The reason that positive and negative voltage regulators are different parts is that they regulate the input voltage by shunting current to ground.
In a LM7805, the input and output are positive with respect to ground; in a LM7905, the input and output are negative with respect to ground. The ground is a single pin that is on both the input and output sides of the regulator, which makes them non-isolated. This is the critical reason they must come in positive and negative versions, unlike "lab power supplies", which are isolated from their inputs.
The better analogy to understand voltage is "repository of potential energy", similar to height for gravitational potential energy. When Galileo dropped his weights from the tower, they were forced downward because their height above the ground (above "zero") gave them potential energy that could be released. After they were lying on the ground, they could fall no farther because no potential energy above the ground remained. Yet if there were a well, they could fall down into it because moving to a negative height releases yet more potential energy. Potential energy can't be seen or measured directly, so it naturally may be negative, like a book-keeping entry. The position chosen to be called "zero" is somewhat arbitrary.
With electrical fields, too, the zero is arbitrary*, or better call it a selected reference point. A charge at a region where the field is high feels a force towards regions where it is low: at the moment you connect a wire across the terminals of a 9V battery, the field is 9V higher at the (+) side compared to the (-) side. We select which point to call our "zero": we can measure with the reference point at the (+) side, in which case the (-) side is -9 volts; or we can measure with the reference point at the (-) side, in which case the (+) side is +9 volts; or we can measure with the reference point in the exact middle of the wire, in which case the (+) side is +4.5 volts and the (-) side is -4.5 volts. Only the voltage difference between two points has any effect on the movement of charges (current).
* It is possible to measure the electric field absolutely using electrometers, but this type of measurement is specialized and not often required. There is an analogous "absolute zero height" in gravitation, which is far out in interstellar space: again, not often used.