They look like the same thing, but their definitions are confusing. Additionally, while it's possible to use 'tolerance'< 0.05 in AIMS easily, in ASE, some structures never optimize if you choose fmax < 0.05. If they are the same thing, one should use the same value for both codes for comparison of the results, right?
I put their explanations from their documentations. These definitions confuse me. In one it says per atom, and in other one, it says all individual atoms
relax_geometry (control.in) Usage: relax_geometry type tolerance Purpose: Specifies if a structure optimization (geometry relaxation) is requested, and which. type specifies the type of requested structure optimization. Default: none. tolerance: Specifies the maximum residual force component per atom (in eV/Å) below which the geometry relaxation is considered converged. - FHI-aims Manual
The convergence criterion is that the force on all individual atoms should be less than fmax: - https://wiki.fysik.dtu.dk/ase/ase/optimize.html