In short — in today’s market, there is practically no difference.

Historically, these terms were used to distinguish between two different technologies, but the industry has since moved toward a single standard:

• How it used to be: VPS (Virtual Private Server) typically referred to virtualization at the operating system level (e.g., OpenVZ). This came with limitations, such as shared resources and the inability to modify the OS kernel. VDS (Virtual Dedicated Server) referred to hardware-level virtualization (KVM), providing complete independence.
• The current state: OS-level virtualization is now almost obsolete among professional providers. Nearly all modern solutions are built on hardware virtualization (KVM, VMware, etc.).
• The industry standard: Today, the terms have become synonymous. Most providers simply use the term VPS to describe the service, regardless of the underlying technical nuances.