The surface-spin magnetism of the antiferromagnetic (AFM) material NiO in nanoparticle and bulk morphology was investigated by magnetic measurements (temperature-dependent zero-field-cooled (zfc) and field-cooled (fc) dc susceptibility, ac susceptibility and zfc and fc hysteresis loops). We addressed the question of whether the multisublattice ordering of the uncompensated surface spins and the exchange bias (EB) effect are only present in the nanoparticles, originating from their high surface-to-volume ratio or if these surface phenomena are generally present in the AFM materials regardless of their bulky or nanoparticle morphology, but the effect is just too small to be detected experimentally in the bulk due to a very small surface magnetization. Performing experiments on the NiO nanoparticles of different sizes and bulk NiO grains, we show that coercivity enhancement and hysteresis loop shift in the fc experiments, considered to be the key experimental manifestations of multisublattice ordering and the EB effect, are true nanoscale phenomena only present in the nanoparticles and absent in the bulk.