The main difference lies in virtualization type. VPS (Virtual Private Server) typically uses container-based virtualization (like OpenVZ) that shares the same kernel, allowing for easy scaling without rebooting — but it limits OS choice and kernel modification.
VDS (Virtual Dedicated Server), on the other hand, uses full hardware virtualization (like KVM), providing complete isolation and the ability to modify the kernel. However, changing resources may require a reboot.
Your choice depends on the level of flexibility and isolation you need.