The Get-Metric returns metric information, but it only shows the metric's Label, not the Key.
While on the Get-Stat cmdlet the Stat parameter expects the Key.
On Get-Metric one has to use
Get-Metric -MetricGroup 'CPU' -Name 'Core Utilization'
This returns all Rollup types (see PCLI-I-226 for that issue), but there is no property that provides the Key (which is 'coreUtilization'.
On Get-Stat one would need to provide
Get-State -Stat 'cpu.coreutilization.average'