Context. Debris discs are populated by belts of planetesimals, whose structure carries dynamical imprints of planets and the formation and evolutionary history of the planetary system. The relatively faint emission of debris discs has previously made it challenging to obtain a large sample of high-resolution ALMA images to characterise their substructures. Aims. The ALMA survey to Resolve exoKuiper belt Substructures (ARKS) was recently completed to cover the lack of high-resolution observations and to investigate the prevalence of substructures such as radial gaps and rings in a sample of 24 debris discs. This study characterises the radial structure of debris discs in the ARKS programme. Methods. We modelled all discs with a range of non-parametric and parametric approaches, including those that deconvolve and deproject the image or fit the visibilities directly, in order to identify and quantify the disc substructures. Results. Across the sample we find that of the 24 discs, 5 host multiple rings, 7 are single rings that display halos or additional low-amplitude rings, and 12 are single rings with at most tentative evidence of additional substructures. The fractional ring widths that we measured are significantly narrower than previously derived values, and they follow a distribution similar to the fractional widths of individual rings resolved in protoplanetary discs. However, there exists a population of rings in debris discs that are significantly wider than those in protoplanetary discs. We also find that discs with steep inner edges consistent with planet sculpting tend to be found at smaller (<100 au) radii, while more radially extended discs tend to have shallower edges more consistent with collisional evolution. An overwhelming majority of discs have radial profiles that are well-described by either a double power law or double-Gaussian parametrisation. Conclusions. While our findings suggest that it may be possible for some debris discs to inherit their structures directly from pro-toplanetary discs, there exists a sizeable population of broad debris discs that cannot be explained in this way. Assuming that the distribution of millimetre dust reflects the distribution of planetesimals, mechanisms that cause rings in protoplanetary discs to migrate or debris discs to broaden soon after formation may be at play, possibly mediated by planetary migration or scattering.