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 correlation between the events is impossible.

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.

Let's put it very simple:
(distances mean spatial distances)

time-like: if you are fast enough, you can be at 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 correlation between the events impossible.

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 correlation between the events is impossible.