According to the Logos wiki,
In 2006, Walt Disney Pictures started using a new intro with a new CGI
animation with a very complex depiction of the Sleepy Beauty Castle
and its surroundings. It was a clear change from the old blue and
white intro with its stylized castle and 2D animation.
The new intro was first used on Pirates of the Caribbean: Dead Man's
Chest, which premiered in the United States on July 7, 2006.
Starting with The Muppets, "WALT" and "PICTURES" have been removed
from the logo.
2006 is the year that Disney repurchased Pixar, and the year after Robert Iger took over Disney. There is a Pixar Disney introduction but, oddly, this new intro was not created by Disney studios, but by Weta Digital in New Zealand.
More information comes from closinglogos.com:
On a night sky background, we see a star, a la Pinocchio. Then, some
clouds appear, a la Mary Poppins, and a pirate ship, a la Peter Pan.
We then see the castle, done in CGI, while different fireworks are
appearing. A circular line is drawn over the castle (in the same vein
as the previous logo), then the castle enters many dots from the
bottom of the screen to reveal "Walt Disney", in the post-1979 Disney
script logo font, albeit slightly revised. "PICTURES" fades in, while
the circular line is nearly staying visible on the logo.
The train could reference Dumbo, but I have not found confirmation of this.
(about 12 minutes into the film)