Observations of black hole binaries (BHBs) have established a rich phenomenology of X-ray states. The soft states range from the low variability, accretion disc dominated thermal (TD) state to the higher variability, non-thermal steep power law (SPL) state. The disc component in all states is typically modelled with standard thin disc accretion theory. However, this theory is inconsistent with optical/UV spectral, variability and gravitational microlensing observations of active galactic nuclei (AGNs), the supermassive analogues of BHBs. An inhomogeneous disc (ID) model with large (≃0.4 dex) temperature fluctuations in each radial annulus can qualitatively explain all of these AGN observations. The inhomogeneity may be a consequence of instabilities in radiation-dominated discs, and therefore may be present in BHBs as well. We show that ID models can explain many features of the TD and SPL states of BHBs. The observed relationships between spectral hardness, disc fraction and rms variability amplitude in BHBs are reproduced with temperature fluctuations similar to those inferred in AGNs, suggesting a unified picture of luminous accretion discs across orders of magnitude in black hole mass. This picture can be tested with spectral fitting of ID models, X-ray polarization observations and radiation magnetohydrodynamic simulations. If BHB accretion discs are indeed inhomogeneous, only the most disc-dominated states (disc fraction ≳0.95) can be used to robustly infer black hole spin using current continuum fitting methods.