In order to test the recently proposed classification of the radio/X-ray states of the X-ray binary Cyg X-3, we present an analysis of the radio data available for the system at much higher spatial resolutions than used for defining the states. The radio data set consists of archival VLBA data at 5 or 15 GHz and new e-EVN data at 5 GHz. We also present 5 GHz MERLIN observations of an outburst of Cyg X-3. In the X-ray regime we use quasi-simultaneous with radio, monitoring and pointed RXTE observations. We find that when the radio emission from both jet and core is globally considered, the behaviour of Cyg X-3 at milliarcsecond scales is consistent with that described at arcsecond scales. However, when the radio emission is disentangled in a core component and a jet component the situation changes. It becomes clear that in active states the radio emission from the jet is dominating that from the core. This shows that in these states the overall radio flux cannot be used as a direct tracer of the accretion state.