Names and History
Although the idea of a black hole dates back to the 18th century, black holes didn't make any headway until Einstein's 1915 general relativity theory, showing that gravity affects light. Work from Karl Schwarzschild in 1916 advanced black hole knowledge, resulting in static black holes eventually being named "Schwarzschild Black Holes." Work from Roy Kerr in the 1960s led to the discovery of a rotating black hole, also known as "Kerr Black Holes."
Charge
One of the basic theories behind both types of black holes states that rotating black holes are charged, while static black holes lack charge. Within rotating black holes (which contain both an inner and outer horizon) the charge is thought to flow from the outer to the inner horizon. Static black holes lack the outer horizon, as well as the charge. Relatively little is known about the charges of black holes.
Angular Momentum
The term "black" stems from the power of the black hole; namely, that they contain an internal gravity so powerful that they suck up all the light that enters the horizon of the black hole. One term applicable to only rotating black holes is "angular momentum," which describes the angular inertia occurring because of the black holes' rotation and mass. Static black holes -- although they contain the intense mass and gravitational pull -- lack angular momentum.
Event Horizons
The event horizon -- although not completely understood -- acts as the boundary line of the black hole. Cross the boundary and even light doesn't have the ability to escape. The thought is that the light cycles towards a center point of the black hole known as the "singularity," which also remains a mystery. Static holes contain one event horizon; however, rotating black holes are suspected of having two different event horizons, an inner one and an outer one.