I haven't heard about this 'oni and the great bird' story before. It would be great if you could give some more details like where you heard about it, or if there are any key elements in the story that you can remember. This would help me to better answer your question.
As I'm not aware of the actual 'oni and the great bird' story, it's difficult to say for sure. However, in general, in a story named like this, the oni, which is likely to be some sort of supernatural being, and the great bird are likely to be the central figures. There may also be characters related to the environment they are in, like people living in the area where the oni and the bird interact, or other magical creatures if it's a fantasy - style story.
I'm not sure which specific 'bird catcher' story you are referring to. There could be many tales about bird catchers in different cultures and literatures. It might be a local folktale, a story from a particular book, or something else.
The Angry Bird full story begins with a happy and harmonious life of the birds on their island. However, one day, the pigs invaded their territory. These pigs are not friendly at all and are only interested in the birds' eggs. The birds, being protective of their eggs, decide to fight back. There are different kinds of birds in the game. The big red bird is like the leader, strong and can cause a good amount of damage when it hits the pigs' structures. The green bird can boomerang back which gives it an advantage in attacking from different angles. As the story unfolds, we see the birds launching themselves from slingshots towards the pigs' forts in order to get their eggs back and teach the pigs a lesson.
Well, the story of the Adarna bird is a long and interesting one. The three princes set out to find the Adarna bird. It has a very special power. As they journey, the eldest prince tries to take the bird but gets cursed because of his bad attitude. The second prince doesn't fare much better. However, the youngest prince is different. He treats the bird with respect. There are also parts in the story where they encounter strange creatures and difficult situations. And ultimately, the youngest prince gets to bring the bird back successfully.
Well, without more details about this 'little bird story', it's hard to tell the full story. It might be a story where the little bird overcomes some difficulties, like facing a big storm but still manages to survive. Maybe it's also about how the little bird discovers new things in its environment, such as a beautiful meadow full of flowers.
In the Angry Bird full story, first, the pigs arrive on the birds' island and steal their eggs. After that, the birds start their counter - attack. Each bird's unique ability comes into play during these attacks. For example, the blue birds splitting helps in covering more area when attacking the pigs' structures. And the battle between the birds and the pigs with their forts and defenses is a continuous main event throughout the story.
The main events are the king getting sick which starts the quest. Then the three sons' attempts to catch the Adarna bird. The eldest son fails and is put to sleep. The second son also has problems. And finally, the youngest son catches the bird and heals the king.