You might be asking yourself if the Climax and The End aren't the same thing.
The answer is: Not always.
Do you remember the graph for the three act structure of a story (which is more or less ubiquitous in Western literature)? Do you remember how the chart had a high point (the Climax) then a steep decline after that?
That decline is called the Falling Action or Descending Action, and could reasonably be called part of The End. For our purposes, we'll say they're part and parcel of that section of the story, because when the Climax is not the end, then there's Falling Action immediately before the actual end of the story.
In more understandable terms, what that means is that the Tension in the story starts at the beginning relatively low, and the Tension is gradually built up throughout the story as the stakes get higher and the heroes get closer to their goal. The stakes are highest at the Climax, where failure could mean death or destruction of an important place or object. When the heroes succeed (as they usually do, one way or another) the Tension is released, but often the story isn't quite done.
For example, when looking at Clash of Kings in the Song of Ice and Fire series, the Climax is near the end of the book, when we realize that Tyrion Lannister is still alive, and the battle was won. But the story for that book isn't yet done, so you find yourself tagging along with Tyrion as he contemplates the way things have changed and what should happen next. The stakes at that point in the story are (relatively) low, as none of the characters are in active danger at that point. The Descending Action takes place as Tyrion realizes that he's no longer in active danger, and The End happens when he concludes his thoughts on the current situation. Nothing else really happens, but some things are addressed.
Similarly, in Harry Potter and the Philosopher's Stone, the Climax happens at Hogwarts, during the battle with Voldemort. When Harry wakes in the hospital wing to the realization that he survived, the Falling Action begins, and questions are answered as he recovers. The End doesn't come until the following chapter, where Harry is sent home for the summer, and walks away from the train station with his aunt and uncle.
This period of Falling Action is important for the same reason that it's important for a diver to adjust the amount of air in his lungs as he swims for the surface. If you think of Tension as pressure applied on the audience, then you can see how a sudden release of that pressure and an abrupt end could leave them feeling disoriented, rather than satisfied. The Falling Action and The End separate from the Climax allow the readers to adjust to the new status quo of lowered Tension and lower stakes. This is especially important (or so thinks I) for stories where there will or might be a delay between reading the end of this story and the beginning of the next.
The End is the section of the story reserved for wrapping up loose ends after the Climax and preparing the reader/player/viewer either for the conclusion or for a sequel. Note that just because you're planning a sequel does not require the previous story's ending to be a cliffhanger. For a good example of a non-cliffhanger ending to a book designed to be part of a series, take a look at any singular book in the Redwall series by Brian Jacques.
To the previous Element
To the next Element