Once on-premises users are synced to Azure AD, you can allow on-premises users to authenticate to Azure AD. If you federate on-premises Active Directory with an Azure AD tenant, you can allow the on-premises user to authenticate to Azure AD.

You can authenticate to Azure ADDS using on-premises credentials. Also, you can authenticate to Azure AD using Azure ADDS credentials.

Reference https://docs.microsoft.com/en-us/azure/active-directory-domain-services/active-directory-ds-synchronization