Semantically they are the same (in their meaning)
Syntactically (in their form) the emphasis is different.
In the first sentence "family" is the most important aspect of the sentence not "success". This makes a lot more sense if this person was already talking about her family and it was added that they are responsable for her success.
In the second sentence success is the important word. So she credits her success to her family and if the sentence were to continue she could talk about more things that make her successful ( not just her family)
In linguistics word order is very important and it has an effect on the ideas trying to be portrayed, even at a very minute level. Look at the words that follow the verbs, this should help a lot. In the first sentence it is her family and in the second it is success.
I hope this helps you understand some of the nuances of your example.
-Mark.