Cells have developed different mechanisms to respond to stress, including the formation of cytoplasmic foci known as stress granules (SGs). SGs are dynamic and formed as a result of stress-induced inhibition of translation. Despite enormous interest in SGs due to their contribution to the pathogenesis of several human diseases, many aspects of SG formation are poorly understood. SGs induced by different stresses are generally assumed to be uniform, although some studies suggest that different SG subtypes and SG-like cytoplasmic foci exist. Here, we investigated the molecular mechanisms of SG assembly and characterized their composition when induced by various stresses. Our data revealed stress-specific differences in composition, assembly and dynamics of SGs and SG-like cytoplasmic foci. Using a set of genetically modified haploid human cells, we determined the molecular circuitry of stress-specific translation inhibition upstream of SG formation and its relation to cell survival. Finally, our studies characterize cytoplasmic stress-induced foci related to, but distinct from, canonical SGs, and also introduce haploid cells as a valuable resource to study RNA granules and translation control mechanisms.