Azure Directory Services

Azure Active Directory (Azure AD) is a directory service that enables you to sign in and access both Microsoft cloud applications and cloud applications that you deploy.
For on-premises environments, Active Directory running on Windows Server provides an identity and access management service that's managed by your organization.
Azure AD is Microsoft's cloud-based identity and access management service.
When you connect On-premises Active Directory with Azure AD, Microsoft can monitor suspicious sign-in attempts from unexpected locations or unknown devices. This feature is available at no extra cost.

Azure AD Services

Azure AD provides services such as:

Authentication: Verifying identity to access applications and resources. It also includes providing functionality such as self-service password reset, multifactor authentication, a custom list of banned passwords, and smart lockout services.
Single sign-on: Single sign-on (SSO) enables you to remember only one username and one password to access multiple applications. A single identity is tied to a user, which simplifies the security model. As users change roles or leave an organization, access modifications are tied to that identity, which greatly reduces the effort needed to change or disable accounts.
Application management: You can manage your cloud and on-premises apps by using Azure AD. Features like Application Proxy, SaaS apps, the My Apps portal, and single sign-on provide a better user experience.
Device management: Along with accounts for individual people, Azure AD supports the registration of devices. Registration enables devices to be managed through tools like Microsoft Intune. It also allows for device-based Conditional Access policies to restrict access attempts to only those coming from known devices, regardless of the requesting user account.

Azure AD is for:

IT administrators: Administrators can use Azure AD to control access to applications and resources based on their business requirements.
App developers: Developers can use Azure AD to provide a standards-based approach for adding functionality to applications that they build, such as adding SSO functionality to an app or enabling an app to work with a user's existing credentials.
Users: Users can manage their identities and take maintenance actions like self-service password reset.
Online service subscribers: Microsoft 365, Microsoft Office 365, Azure, and Microsoft Dynamics CRM Online subscribers are already using Azure AD to authenticate into their account.

If you had an on-premises environment running Active Directory and a cloud deployment using Azure AD, you would need to maintain two identity sets.
You can connect Active Directory with Azure AD, enabling a consistent identity experience between cloud and on-premises.
Azure AD Connect synchronizes user identities between on-premises Active Directory and Azure so you can use features like SSO, multifactor authentication, and self-service password reset under both systems.

Azure Active Directory Domain Services (Azure AD DS) is a service that provides managed domain services such as domain join, group policy, lightweight directory access protocol (LDAP), and Kerberos/NTLM authentication.
Just like Azure AD lets you use directory services without having to maintain the infrastructure supporting it, with Azure AD DS, you get the benefit of domain services without the need to deploy, manage, and patch domain controllers (DCs) in the cloud.
An Azure AD DS managed domain also lets you run legacy applications in the cloud.
Azure AD DS integrates with your existing Azure AD tenant. This integration lets users sign into services and applications connected to the managed domain using their existing credentials. You can also use existing groups and user accounts to secure access to resources. These features provide a smoother lift-and-shift of on-premises resources to Azure.

When you create an Azure AD DS managed domain, you define a unique namespace. This namespace is the domain name.
Two Windows Server domain controllers are then deployed into your selected Azure region. This deployment of DCs is known as a replica set.
You don't need to manage, configure, or update these DCs. The Azure platform handles the DCs as part of the managed domain, including backups and encryption at rest using Azure Disk Encryption.
A managed domain is configured to perform a one-way synchronization from Azure AD to Azure AD DS. You can create resources directly in the managed domain, but they aren't synchronized back to Azure AD.
In a hybrid environment with an on-premises AD DS environment, Azure AD Connect synchronizes identity information with Azure AD, which is then synchronized to the managed domain.