When initially spawned in, Ender Dragons flap their wings rapidly and circle a small area around where they were spawned (breaking blocks if any are there). But after taking a significant amount of damage from the player, they will eventually revert to the same behavior as the one in the End.
I'm not sure which behavior is intended, but I don't think switching mid fight is correct.
Steps to reproduce:
Get an Ender Dragon spawn egg and use it (preferably not in the End)
Observe the Dragon's behavior
Fight the Dragon (Bow, Crossbow, or Trident recommended)
After a while, the Dragon will change behavior. You will know when this happens because the Dragon will greatly reduce its flapping speed (as well as hightailing off toward (0,0) if it isn't already near there).
Notice that the Dragon is now acting like the one in the End
The dragon always acts like the one in the end; it heads to 0 0 because it selected it's dragon breath attack, which means going to 0 0 (the portal location) to sit on the bedrock.