We study different types of stationary dynamos observed in the Von Kármán sodium (VKS) experiment when varying the electromagnetic boundary conditions on (and in) the impellers. The flow is driven with two impellers made of soft iron (Monchaux et al 2007 Phys Rev. Lett. 98 044502) or using one soft-iron impeller and one stainless steel impeller. The magnetic field is mapped using 40 three-dimensional probes distributed within the flow and its surroundings. Symmetry and coupling properties are then retrieved from direct probe measurements and/or from the field structure as reconstructed using the inversion procedure described by Boisson and Dubrulle (2011 New J. Phys. 13 023037). Several salient results are obtained: (i) dynamo action is not achieved unless at least one iron impeller is rotating, at a frequency larger than 15 Hz; (ii) the resulting dynamo is a dipolar, mostly axisymmetric structure; and (iii) the self-sustained magnetic field properties depend on the sodium flow structure between the two impellers. We propose to interpret the stationary dynamos generation as the (constructive or destructive) superposition of two one-impeller fluid dynamos generated close to the soft-iron impellers, nonlinearly coupled through the turbulent flow, as suggested by Verhille et al (2010 New J. Phys. 12 033006). The normal form equation describing this coupling is similar to the one obtained in a theoretical model (Pétrélis et al 2009 Phys. Rev. Lett. 102 144503).