tolkiens legendarium - How did Bilbo Baggins find the One Ring exactly?

In the Fellowship of the Ring movie, it explains how Bilbo got the Ring:

Its time had now come. It abandoned Gollum. But then something happened that the Ring did not intend. It was picked up by the most unlikely creature imaginable. A hobbit, Bilbo Baggins, of the Shire.

In The Hobbit: An Unexpected Journey movie, Bilbo and a goblin fall after they fight. Bilbo wakes up under the mushrooms, the goblin is unconscious. Bilbo sees Gollum. He tries to drag the goblin to his own place for eating. The goblin struggles and Gollum starts to hit it until it dies. In this fight, the One Ring falls from Gollum's pocket. Gollum starts to drag the now unconscious goblin. Bilbo waits until he leaves, he stands up, picks his sword under the mushrooms and then see the Ring. He takes it and puts it in his pocket.

From The Hobbit: Book and Film Differences blog:

The Book: Bilbo awakens in total darkness; it's so dark he literally cannot tell the difference between having his eyes open or closed. He gropes around on all fours, and his hand accidentally brushes against a small ring of cold metal. He puts it in his pocket without thinking and continues on his way. He sits down for a moment. He feels for his pipe, then for his tobacco, but cannot find a match. That's the last straw for Bilbo Baggins' hopes, and he despairs for a moment. He draws his sword, and noticing that it "shone pale and dim before his eyes," found enough hope to continue. Using his sword as a source of light, he trots along.

Also there is a video from youtube which explain my question.

In my opinion, these three stories are quite different. I don't expect they all should be exact the same but I didn't expect they will be quite different.

Is there any reason makes this situation different each other in films and movies?

Answer

I don't think those three stories are particularly different. They all share the same core: Bilbo gets lost in the caves beneath the Misty Mountains, where he finds the Ring, after it was dropped by Gollum (or, more precisely, where it dropped itself away from Gollum). This is the essence - the ring wanted to leave Gollum and be picked up by someone else to take it away, and it was.

The rest is incidental - does it really matter if Bilbo groped around in the dark and found it, or saw it on the ground and found it? Does it matter if we saw the Ring fall from Gollum's pocket or only seen the end result of it? Not really. The essence remains the same.

As for the reasons for the differences - groping around blindly in the dark can make for a good narrative in a book, but is quite boring to see on screen. It's not surprising that Peter Jackson decided to liven it up with some action. And as for the bit in The Lord Of The Rings - well, it's merely an overview, not a detailed scene. Bilbo found it. End of story.