Toys coming alive, worlds of fantasy within normal worlds, innocence and growing up, childhood preceding school. By summary and even in many ways by theme, Toy Story is like a modern Winnie the Pooh. Christopher Robin becomes Andy, Winnie the Pooh becomes Woody, Tigger is somewhat like Buzz (in the fact that he is the "newcomer"), Kanga is like Bo in that (initially, at least) they are both the female character among many male characters, and so on.
Though Christopher Robin is actually with his toys when they walk and talk in the Hundred Acre Wood, and Andy's toys only move when he isn't around, both have their special relationship with their toys. And the Winnie the Pooh books do progress from the toys'/animals' perspectives rather than Christopher Robin's; he steps in and out of the woods, but they stay and live their "lives" there, just like Andy's toys have their own goings on.
But it's the combination of innocence and tragedy (similar to Peter Pan, but not so intense as that most sad of all stories) that unites these two stories most. At the end of The House on Pooh Corner, Christopher Robin has to say goodbye to his world of children's toys--he's going to school and knows things won't be the same anymore; it's a very bittersweet moment he has with Winnie the Pooh at the end. Andy, too, struggles with letting go of his childhood companions, though the way he deals with it is in knowing that their stories will live on in someone else's childhood life.
No wonder children's stories can be so touching and so complicated and real.