We characterize the properties and evolution of bright central galaxies (BCGs) and the surrounding intracluster light (ICL) in galaxy clusters identified in the Dark Energy Survey and Atacama Cosmology Telescope Survey (DES-ACT) overlapping regions, covering the redshift range 0.20 < z < 0.80. Over this redshift range, we measure no change in the ICL's stellar content (between 50 and 300 kpc) in clusters with log10(M200m,SZ/M⊙) >14.4. We also measure the stellar mass-halo mass (SMHM) relation for the BCG+ICL system and find that the slope, β, which characterizes the dependence of M200m,SZ on the BCG+ICL stellar mass, increases with radius. The outskirts are more strongly correlated with the halo than the core, which supports that the BCG+ICL system follows a two-phase growth, where recent growth (z < 2) occurs beyond the BCG's core. Additionally, we compare our observed SMHM relation results to the IllustrisTNG300-1 cosmological hydrodynamic simulations and find moderate qualitative agreement in the amount of diffuse light. However, the SMHM relation's slope is steeper in TNG300-1 and the intrinsic scatter is lower, likely from the absence of projection effects in TNG300-1. Additionally, we find that the ICL exhibits a colour gradient such that the outskirts are bluer than the core. Moreover, for the lower halo mass clusters (log10(M200m,SZ/M⊙) < 14.59), we detect a modest change in the colour gradient's slope with lookback time, which combined with the absence of stellar mass growth may suggest that lower mass clusters have been involved in growth via tidal stripping more recently than their higher mass counterparts.