Are both Azure AD service and Azure AD instance means the same?
As Phil mentions, yes. Pretty much. And instance is a specific implementation of the service. If you talk about services, it is a general statement, where instance is a specific one.
Active Directory Domain Services (AD DS) – Enterprise-ready lightweight directory access protocol (LDAP) server that provides key features such as identity and authentication, computer object management, group policy, and trusts.
AD DS is a central component in many organizations with an on-premises IT environment, and provides core user account authentication and computer management features.
For more information, see Active Directory Domain Services overview in the Windows Server documentation.
Azure Active Directory (Azure AD) – Cloud-based identity and mobile device management that provides user account and authentication services for resources such as Microsoft 365, the Azure portal, or SaaS applications.
Azure AD can be synchronized with an on-premises AD DS environment to provide a single identity to users that works natively in the cloud.
For more information about Azure AD, see What is Azure Active Directory?
Azure Active Directory Domain Services (Azure AD DS) – Provides managed domain services with a subset of fully-compatible traditional AD DS features such as domain join, group policy, LDAP, and Kerberos / NTLM authentication.
Azure AD DS integrates with Azure AD, which itself can synchronize with an on-premises AD DS environment. This ability extends central identity use cases to traditional web applications that run in Azure as part of a lift-and-shift strategy.
To learn more about synchronization with Azure AD and on-premises, see How objects and credentials are synchronized in a managed domain.