What is the difference between these two api ?
Azure AD Graph API
https://msdn.microsoft.com/en-us/library/azure/ad/graph/api/api-catalog
Microsoft Graph supports most of the directory features that Azure AD Graph supports, but not all.
Here is some information for you to refer.
1.The two APIs have different endpoints.
2.Client libraries
3.For more gaps between Microsoft Graph and Azure AD Graph, you could refer to this article.
Note: The time of the article is May 10, 2017, you could refer to Changelog for Microsoft Graph to see some feature was or not been updated.