The present study compares the ionic wind produced by volume DC and AC corona discharges, and by surface dielectric barrier discharges (DBD). On the one hand, in the case of a volume corona discharge ignited between a high-voltage needle and a grounded plate, our measurements highlight that the ionic wind velocity increases in the presence of positive breakdown streamers. On the other hand, in the case of a surface AC DBD, the ionic wind velocity decreases when streamers occur. Why such a difference? The answer is not easy and the debate remains open. However, one answer would be that the streamers occurring in a volume needle-to-plate discharge leave an abundance of positive ions in the inter-electrode space and that these ions drift because of the electric field, just after the streamer propagation. On the other hand, in the case of a surface DBD, the streamers can leave positive ions in their wake but their heads especially deposit positive ions at the location where they stop propagating, i.e. a few millimetres from the electrode (up to about 10–15 mm). Then this positive space charge deposited at a few millimetres from the active electrode edge on the dielectric surface acts as a screen against the electric field due to the applied high voltage, thus preventing the drift of the ions remaining on the surface of the dielectric, close to the electrode edge. Having said that, the reality is that this explanation is certainly very simplistic compared with the very complex phenomena taking place in these two discharges, particularly at the times when the streamers form and propagate.