What is the difference between ordinary-spacial cloaking and spacetime cloaking? I am unsure of what are the differences between space time cloaking and spacial cloaking, as any event can be hidden from a viewer using spatial cloaking for however long the cloaking is activated, from my understanding. What is the difference between these two types of cloaking?
 A: Going purely off of my limited reading of the Wikipedia articles linked to in the question, the methods of cloaking are not so different in terms of their overall goal and end result. They are both cloaking mechanisms, so they ultimately achieve the same thing in terms of hiding an object/event, but their "sub-goals" are different.
Spatial cloaking is the simpler of the two cloaking methods you ask about. The sub-goal is to just move light around an object to be cloaked.
Space-time cloaking's sub-goal deals with hiding events that occur at certain times. It aims to move different light signals at different speeds so that one signal arrives before the event to be hidden and the other arrives later. Then, the fast signal is slowed and the slow signal is sped up so that overall there is no observed interruption.
The analogies with traffic on Wikipedia are pretty useful, I think. Imagine that we have a highway with cars (light) traveling down it. Spatial cloaking is like if we had an island placed in the middle of the highway that we want to hide from someone farther down the highway. We would just "reconstruct" the highway to split before the island, and then come back together behind the island. Someone farther down the highway would then not be able to tell that the island was present based on the flow of cars.
Space-time cloaking is like if we wanted to instead hide from someone farther down the highway the event of a pedestrian crossing the highway. We would then speed up one section of traffic and slow down another section of traffic. This would allow the pedestrian to cross the highway. Then we would speed up the slowed down traffic and slow down the sped up traffic. This would result in an unaffected traffic flow as observed by someone farther down the highway, and cloaking would have been achieved.
Of course, we could use a "spatial traffic cloak" in the case of the crossing pedestrian so that we have the traffic just go around the pedestrian altogether. But this is what I was discussing at the beginning: the difference really isn't in the end result but rather in the method itself.
