Let's put it **very simple**: They tell you "how far something is apart compared to c"  

**time-like**: if you are fast enough, you can be at (think spatial, like "at the festival") event a **and** at event b, it is only a "matter of time" until you see the second event

**space-like**: the two events are too far apart (in space). You cannot see both of them together, no matter how fast you are. As soon as event a happened and you go as fast as possible, event b will have happened before you arrive there.

**light-like**: exactly in between, the events are so far away that if you are as fast as light, you can see both events. If they are further away, they become *space-like*, if they are closer they become *time-like*

So a space-like separation makes *any* causal relation between the two events impossible, i.e. one _cannot_ cause or influence the other.$^1$


_1) as mentioned, a common cause (an event that is time-like to both events) can still make the two correlated._