In DFT calculations, shift values define whether the k-point grid is centered at Γ (0 0 0) or shifted (e.g., 1 1 1). In metallic systems like bcc iron, using a shifted grid usually improves Brillouin zone sampling and leads to faster convergence of properties like Fermi energy and magnetization. Without a shift, you may need a denser k-point mesh to achieve the same accuracy. Shifts are especially important for metals due to the sharp Fermi surface, but less critical for insulators or when specific symmetry points are needed (e.g., band structure at Γ).

As pointed out in the previous question, the shift might improve or not the convergence of the sampling of the Brillouin Zone. This might be system dependent so there is not an a-priori answer. However, once convergence is achieved with or without the shift, the other physical quantities should be the same in both case.

That said, small differences (for example in the Fermi energy) could persist due to the fact that you are possibly not sampling the maximum of the valence band or the minimum of the conduction band.

I hope this helps,

Roberto