ABSTRACT We use the TNG50 from the IllustrisTNG suite of cosmological hydrodynamical simulation, complemented by a catalogue of tagged globular clusters, to investigate the properties and build up of two extended luminous components: the intra-cluster light (ICL) and the intra-cluster globular clusters (ICGCs). We select the 39 most massive groups and clusters in the box, spanning the range of virial masses $5 \times 10^{12} \lt \rm M_{200}/\rm {\rm M}_{⊙ } \lt 2 \times 10^{14}$. We find good agreement between predictions from the simulations and current observational estimates of the fraction of mass in the ICL and its radial extension. The stellar mass of the ICL is only $∼ 10~{{\ \rm per\ cent}}$–20 per cent of the stellar mass in the central galaxy but encodes useful information on the assembly history of the group or cluster. About half the ICL in all our systems is brought in by galaxies in a narrow stellar mass range, M* = 1010–1011 M⊙. However, the contribution of low-mass galaxies (M* < 1010 M⊙) to the build up of the ICL varies broadly from system to system, $∼ 5~{{\ \rm per\ cent}}-45~{{\ \rm per\ cent}}$, a feature that might be recovered from the observable properties of the ICL at z = 0. At fixed virial mass, systems where the accretion of dwarf galaxies plays an important role have shallower metallicity profiles, less metal content, and a lower stellar mass in the ICL than systems where the main contributors are more massive galaxies. We show that intra-cluster GCs are also good tracers of this history, representing a valuable alternative when diffuse light is not detectable.