Usually, cell types are found by clustering cells in expression space (or some lower dim. projection of it), and calculating differentially expressed (DE) genes. These DE genes are then used to annotate the cluster to a particular type. Cell states are then thought of as a 'fine-grained' view on this cluster, making some reference to a biological process.
However, this means that a particular cell state can never be present across cell types, whereas we do think of them like this. For example, "being at a certain point along the cell cycle" can be thought of as a state, or "being under stress", and cells of different types can be in these states simultaneously. Is there some principled way to extract such states from single cell gene-expression data? It should be able to annotate different, far removed regions in expression space as being in the same state, so probably cannot be based on distances in expression space.