A camshaft phaser, including: a gear to receive torque; a housing non-rotatably connected to the gear; and a phase adjustment assembly. The phase adjustment assembly includes: first and second frusto-conical shaped surfaces arranged to non-rotatably connect to a camshaft; third and fourth frusto-conical shaped surfaces; and a displacement assembly. The displacement assembly is arranged to: for an advance mode, displace the first frusto-conical surface in the first axial direction to non-rotatably connect the first and third frusto-conical surfaces and so that the second frusto-conical surface is rotatable with respect to the fourth frusto-conical surface in a first circumferential direction; and for a retard mode, displace the second frusto-conical surface in the second axial direction to non-rotatably connect the second and fourth frusto-conical surfaces and so that the first frusto-conical surface is rotatable with respect to the third frusto-conical surface in a second circumferential direction, opposite the first circumferential direction.