In a sheared steady state, glasses reach a nonequilibrium criticality called yielding criticality. We report that the qualitative nature of this nonequilibrium critical phenomenon depends on the details of the system and that responses and fluctuations are governed by different critical correlation lengths in specific situations. This scale separation of critical lengths arises when the screening of elastic propagation of mechanical signals is not negligible. We also discuss the determinant of the impact of screening effects from the viewpoint of the microscopic dissipation mechanism.