First airline, first type, either pilot can call 'stop' PF retained control and actioned.
First airline second type initially the same until about a year later when a crew had 'communication issues' and the call was misheard by PF so the call was changed to 'stop stop stop'. A year or so later it reverted back to just 'stop' for company commonality.
First airline, third type, as per type one.
Second airline, type one (same type as type three above) still the same.
Second airline, type two (a new type for the airline) The call was 'reject' and only by the captain but the actions were still by PF. Call changed to 'stop' about 18 months later (again for company commonality).
Third airline 'stop' call by captain only and actioned by the captain.