Final answer:
The correct term for extending an on-premises infrastructure into the cloud is 'Hybrid deployment'. This deployment model allows organizations to leverage both on-premises and cloud resources.
Step-by-step explanation:
The deployment term for an environment that extends an existing on-premises infrastructure into the cloud to connect cloud resources to internal systems is called a Hybrid deployment. This type of infrastructure combines both on-premises resources and cloud resources, allowing for a flexible and scalable IT environment. Organizations often adopt a hybrid deployment model as a transitional step in moving some of their IT services to the cloud while keeping sensitive operations secure on their own servers, taking advantage of cloud computing benefits without fully relinquishing control of their data and services.