It is known that there is a link between the theory of seismic interferometry and theories of seismic imaging and inversion. However, although this has been discussed in several studies, there are few where any explicit links have been derived. We use reciprocity theorems for scattering media to derive a new form of seismic interferometry that describes the scattered wavefield between a source and a receiver in an acoustic medium, using both sources and receivers on two enclosing boundaries. This form of seismic interferometry is equivalent to a generalized imaging condition (IC) that combines the full wavefield inside any finite-sized subregion of the medium of interest. By using the Born (single-scattering) approximation, this generalized IC reduces to the method of imaging by double-focusing originally derived by Michael Oristaglio in 1989. Thus an explicit link is made between seismic interferometry, new generalized full-wavefield ICs, and existing single-scattering imaging methods.