Black hole: Something we are certain that exists in RL. Caused by the 'death' of supergiant stars. Look it up on Wikipedia or Google it if you want more info. Alternatively, I will PM you a compact explanation if you so desire.
A black hole is a gravitational singularity. Essentially, there is a 'point' towards which massive gravitational force pulls. Getting caught by a black hole would have your ship being annihilated by the sheer force. This would occur regardless of direction travelled - approaching or attempting to flee the singularity would destroy you. You cannot escape from a Black Hole.
Wormhole: The thing that is the 'gap' or 'bridge' between two points in space. When travelling by Jump Holes or Gates, you are considered to be travelling through a wormhole.
Jump Hole: The name for the naturally-occuring phenomena which create wormholes across the Sirius Sector.
Jump Gate: A device which creates an artificial wormhole that behaves very similarly to a Jump Hole.
________
Flying through Jump Holes in Sirius: As demonstrated in Vanilla Single Player, it's usually a bit dangerous, as you don't know how stable the hole is.
See: fleeing Bretonia; the mission to retrieve the Nomad Power Core.