Can Anyone tell the difference between Azure Active Directory Graph vs Microsoft Graph.
AAD Graph API is an older API that gives access to only directory data.
You should prefer MS Graph API wherever possible.
MS Graph API combines many APIs into one, including those in AAD Graph API.
What is the use of the these API and appropriate scenario to choose these API
Always choose MS Graph API if it works in your case and provides the data you need.
For example with Azure AD B2C you cannot really use MS Graph API.
There may also be some smaller things missing from MS Graph API that exist in AAD Graph API.
Also What is the best approach to call the Graph API (directly from angular application or From Web API)?
Use Implicit Grant flow with MSAL.js from your front-end.
Your front-end app needs to be registered in AAD and require delegated permissions to the API so it can call the API on behalf of the signed in user.