Does the same vulnerability get the same CVSS score on every system?

The basic technical score can be the same, but the local CVSS-BTE score does not have to be. An isolated test environment, an internal workstation, a public identity service and a safety-critical device may differ in accessibility, measures, required protection and consequences for other systems or people.

CVSS 4.0 can capture such differences with Threat and Environmental Metrics. Human safety can also factor directly into the score within the Environmental Metrics. Additional context can also influence the local ranking without changing the number. An internal system does not automatically receive a lower score: every adjustment must follow demonstrable properties of the actual environment. See the metric groups and assessment rules of FIRST.