When do 'being' and 'to be' mean the same and when they not?

Solution 1:

What is traditionally known as the present participle, in spite of its name, gives no time reference.

• Being a lumberjack, he had a hearty appetite.
• Being a lumberjack, he has a hearty appetite.
• Being a lumberjack when he leaves school will mean that he will have a hearty appetite.

So with the sentence given, 'She is excited about being a mother', 'being' does not indicate whether the state is new (not longstanding, or the excitement would be unusual) or anticipated. A present state, or an [anticipated] future state.

But 'She is excited to be a mother' means that she is a recent mother. 'I am happy to be here' likewise addresses an existing state. 'She was happy to be a mother' would address an existing state at the time referred to.