A cloud server is essentially a VPS server.
the differences are subtle and vary based on your definition of what is a 'cloud' . The main differences are:
- Clouds are usually accesible via an API allowing you for dynamic reosurce provisioning
- Clouds have a pay-as-you-go model, while VPS usually has a fixed monthly price that includes certain bandwidth
- VPS is focused on the server/compute with hard disk local storage while clouds usually provide more services such as database, load balancing, networking, etc.