Shear thinning is fundamental to a broad range of particle suspensions, both in nature and in industrial applications. Yet the mechanisms governing it remain unclear. In particular, the distinct, and often competing, roles of the interparticle, particle-fluid interactions and the particle surface morphology need clarity. By using non-Brownian silica particles with different morphology, surface functional groups and suspending media, here we reveal two different shear thinning mechanisms, controlled either by frictional or adhesion forces between particles. Smooth glass sphere suspensions in a polar medium (glycerol), where particles interact strongly with the solvent, showed no shear thinning even at high volume fractions (φ≥0.5), while rough silica particles, with similar size distribution, induced shear thinning behaviour at φ values of 0.25 and above. The latter is attributed to the increased frictional contacts in rough and irregular particles. Considering surface irregularity as elastically deformable asperities enabled us to estimate the critical load above which two neighbouring rough particles experience frictional contacts giving rise to shear thinning. In contrast, in a non-polar (mineral oil) solvent, with which the particles do not interact strongly, both glass spheres and the rough silicas showed a pronounced shear thinning response and yield stress behaviour at volume fractions as low as 2% v/v. The rheology of these suspensions is dictated by the adhesion forces between the particles that lead to the formation of large agglomerates, which breakdown under increasing shear. The evolution of the sheared suspensions microstructure was captured using an optical shearing cell, which also enabled us to quantify the particle agglomeration characteristics using an aggregation index. To demonstrate the generality of our approach, we modified the surface chemistry of the glass spheres by introducing hydrophobic groups (e.g. a fluorosilane or palmitic acid) to inhibit inter-particle interactions and improve the dispersion of the otherwise inherently hydrophilic glass spheres in mineral oil; as expected, this suppressed the shear thinning behaviour of the suspensions. The present results clearly elucidate alternative design routes to controlling suspension rheology, whether to promote or suppress shear thinning, offering new insights for the manufacturing and manipulation of complex particle suspensions.