The nature of the bonding between highly attractive colloids can lead to a profound difference in the structures of aggregates, as revealed through scattering. In particular, colloidal bonds can either be 'shear-rigid', as is the case in classic diffusion limited aggregation (DLA) experiments on solid gold particles, or they can be 'slippery', as we show for attractive dispersions of uniform nanoscale droplets, or 'nanoemulsions', comprised of silicone oil in water. Despite the strong attraction between the oil droplets, which has been induced by adding salt, a thin layer of the continuous phase remains between droplets, precluding coalescence. Slippery attractions occur when the well depth of the secondary minimum is much greater than thermal energy and the range is much smaller than the droplet radius. We use time-resolved small angle neutron scattering (TR-SANS) to study the kinetics of the appearance of peaks related to correlations between nearest neighbor droplets at high wavenumber, q, after abruptly creating an attractive interaction. We show that small dense clusters of droplets are first formed, and these, in turn, aggregate into tenuous fractal networks and gels. Simulations of slippery diffusion-limited aggregation (S-DLA) confirm an earlier hypothesis that attractively jammed tetrahedra of spheres can be considered as the basic building block of space-filling clusters and networks of slippery attractive spheres. The similarity between the computed structure factor, S(q), of S-DLA aggregates and the measured S(q) indicates that slippery DLA is a useful concept for understanding scattering signatures of attractively jammed networks of spheres.