The seems to refer to All entity/entities being referenced. As in the example "The king" it is understood that there is only the one king, but it notes every (instance? example?) of kings which is understood within the statement in which it is made. "The leaders" refers to every member in a group of leaders, of which there is implied only the single group, at least in this context.
That appears to call out a particular party (size 1+) within a larger group, and splits them from the (desires, actions, etc) of the rest of the group, usually for purposes of self. For examples: That faction (of some group) wants (not consistent with the desires of the whole), or That one guy (out of potentially any/all guys known, or unknown) did XYZ. Others might have also done any of X, or Y, or Z, or even some combination thereof, but we don't care about them, because we are only discussing a single person and their actions in this example.
Truth be told, I'm just making this up as I go, so I'm sure there are all sorts of flaws people can find in this. Still, after reading other responses, this appears to be the best summation I can think of, at this time.