Virtualization is software—specifically a hypervisor—that splits one physical server into multiple isolated Virtual Machines (VMs). It maximizes your hardware, but scaling it requires manual setup.
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Cloud computing is the service built on top of that engine. It takes those virtualized resources and delivers them over the internet on demand. Instead of manually configuring hardware, you use a self-service dashboard to scale instantly, paying only for what you use.
​In short:

Virtualization is the core technology that manipulates hardware, while cloud computing is the scalable, pay-as-you-go delivery model it makes possible. You need the engine to drive the car.