We analyze correlated-triplet-pair (TT) singletfission intermediates toward two-triplet separation (T...T) using spin-state-averaged density matrix renormalization group electronic-structure calculations. Specifically, we compare the triplet− triplet exchange (J) for tetracene dimers, bipentacene, a subunit of the benzodithiophene−thiophene dioxide polymer, and a carotenoid (neurosporene). Exchange-split energy gaps of J and 3J separate a singlet from a triplet and a singlet from a quintet, respectively. We draw two new insights: (a) the canonical tetracene singlet-fission unit cell supports precisely three lowlying TT intermediates with order-of-magnitude differences in J, and (b) the separable TT intermediate in carotenoids emanates from a pair of excitations to the second triplet state. Therefore, unlike with tetracenes, carotenoid fission requires above-gap excitations. In all cases, the distinguishability of the molecular triplets that is, the extent of orbital overlapdetermines the splitting within the spin manifold of TT states. Consequently, J represents a spectroscopic observable that distnguishes the resemblance between TT intermediates and the T...T product.