Although we very often see questions written like yours is, that is not the correct way to do it! The colon use is not correct. It's a total abomination!
The correct way to write your question is as follows. And it's much easier to write than the way you did.
What is the difference between "She claimed the child as her own." and "She claimed the child to be her own."?
Because I feel so strongly about the above message, I am not going to dilute it by answering your question now in this post. Someone else or I will respond to your question before long.
Interested in Language