To clarify whether the familial liability to psychosis associated with bipolar disorder (BD) is nonspecific or has a greater effect on risk for psychosis in cases with prominent mood symptoms and/or a remitting course. We examined, in 984 809 offspring raised in intact families in Sweden, born 1980-1996 and followed-up through 2018, by multivariable Cox proportional hazards regression, risk in offspring of parents with BD for 7 psychotic disorders: Psychotic MD (PMD), psychotic BD (PBD), schizoaffective disorder (SAD), acute psychoses, psychosis NOS, delusional disorder (DD) and schizophrenia (SZ). Diagnoses were obtained from national registers. In the offspring of BD parents, the hazard ratios (HR) for these 7 disorders formed an inverted U-shaped curve, rising from 2.98 for PMD, to peak at 4.49 for PBD and 5.25 for SAD, and then declining to a HR of 3.48 for acute psychoses and 3.22 for psychosis NOS, to a low of 2.19 for DD and 2.33 for SZ. A similar pattern of risks was seen in offspring of mothers and fathers affected with BD and in offspring predicted from age at onset in their BD parent. The BD-associated risk for psychosis impacts most strongly on mood disorders, moderately on episodic psychotic syndromes, and least on chronic psychotic disorders. These results support prior clinical studies suggesting a qualitative difference in the familial substrate for psychosis occurring in BD and SZ.