We investigate here the origins of carbonaceous aerosols (Organic and Elemental Carbon) at various French urban sites (Paris, Marseille, Grenoble, ...) using different source apportionment models applied to filter-based (including C and organic tracers), Aerosol Mass Spectrometer, and multi-wavelength Aethalometer measurements. Discrepancies within results of the different receptor models are assessed to be mainly due to differences in the conceptual hypotheses made for each of them. For instance, the Chemical Mass Balance approach aims at apportioning the whole mass of carbon emitted by primary sources whatever the chemical state of primary organic aerosols (unreacted or reacted), while the Positive Matrix Factorization approach applied to AMS measurements is very likely to treat processed/oxidized primary organic aerosols (OPOA) separately from unreacted POA. Results of source apportionment model intercomparisons thus help better understanding the significance of heterogeneous oxidation processes and traditional secondary organic aerosol formation affecting particles of different origin (local vs. regional). The observation of significant discrepancies in some cases (e.g., high influence of biomass burning emissions) also raises the issue whether source apportionment studies should estimate the remaining unreacted constituents of primary emissions or the amount of particulate matter that are related to both unreacted and processed primary emissions.