Detonation nanodiamonds (DNDs) are becoming increasingly important in science and technology with applications from drug delivery to tribology. DNDs are known to self-assemble into fractal-like aggregates in water, but their colloidal properties remain poorly understood. Here, the effect of salt and particle concentration on the size and shape of these aggregates is investigated using dynamic light scattering and small-angle X-ray scattering. Our results suggest the existence of two particle aggregate populations with diameters on the scale of 50 nm and 300 nm, respectively. The concentration of NaCl, in the range 0.005-1 mM, does not have a significant effect on the size or shape of the particle aggregates. The hydrodynamic radius of both aggregate populations decreases as the DND concentration increases from 0.01 to 2 mg mL-1. At the same time, the particle aggregates become denser and their overall shape changes from disk-like to rod-like with increasing DND concentration. We identify unexpected similarities between the aggregate structures observed for DNDs and those commonly observed for concentrated colloidal particles in high salt environments, described by classical colloid aggregation theories. Our results contribute to the fundamental understanding of the colloidal properties of DNDs and pave the way for the engineering of novel nanoparticle-based systems that make use of DNDs' unique colloidal properties for future applications.