Individuals with schizophrenia frequently experience co-occurring substance use, including tobacco smoking and heavy cannabis use, and substance use disorders. There is interest in understanding the extent to which these relationships are causal, and to what extent shared genetic factors play a role. We explored the relationships between schizophrenia (Scz), cannabis use disorder (CanUD), and ever-regular tobacco smoking (Smk) using the largest available genome-wide studies of these phenotypes in individuals of African and European ancestries. All three phenotypes were positively genetically correlated (rgs = 0.17 - 0.62). Causal inference analyses suggested the presence of horizontal pleiotropy, but evidence for bidirectional causal relationships was also found between all three phenotypes even after correcting for horizontal pleiotropy. We identified 439 pleiotropic loci in the European ancestry data, 150 of which were novel (i.e., not genome-wide significant in the original studies). Of these pleiotropic loci, 202 had lead variants which showed convergent effects (i.e., same direction of effect) on Scz, CanUD, and Smk. Genetic variants convergent across all three phenotypes showed strong genetic correlations with risk-taking, executive function, and several mental health conditions. Our results suggest that both horizontal pleiotropy and causal mechanisms may play a role in the relationship between CanUD, Smk, and Scz, but longitudinal, prospective studies are needed to confirm a causal relationship.