The charge-transfer transitions relevant to single- and double-bond photochemical twisting have been studied in the framework of the biradicaloid state theory using the AM1 method for a family of donor-acceptor-substituted stilbenoids and a series of sparkle-simulated model stilbenes. Features in common and mutually interchangeable properties for the two transition types as well as their peculiarities are revealed; they are considered in relation to the varied donor-acceptor strength of the substituents, with particular attention given to the occurrence of S-0-S-1 state conical intersections. The difference in critical points at which the conical intersections occur for double-bond and single-bond twisted stilbenoids is shown to be related to the splitting of the cyanine limit of their planar counterparts.