The mechanisms of triplet energy transfer across the inorganic nanocrystal/organic molecule interface remain poorly understood. Many seemingly contradictory results have been reported, mainly because of the complicated trap states characteristic of inorganic semiconductors and the ill-defined relative energetics between semiconductors and molecules used in these studies. Here we clarify the transfer mechanisms by performing combined transient absorption and photoluminescence measurements, both with sub-picosecond time resolution, on model systems comprising lead halide perovskite nanocrystals with very low surface trap densities as the triplet donor and polyacenes which either favour or prohibit charge transfer as the triplet acceptors. Hole transfer from nanocrystals to tetracene is energetically favoured, and hence triplet transfer proceeds via a charge separated state. In contrast, charge transfer to naphthalene is energetically unfavourable and spectroscopy shows direct triplet transfer from nanocrystals to naphthalene; nonetheless, this "direct" process could also be mediated by a high-energy, virtual charge-transfer state.