Alfvénic fluctuations in solar wind are an intrinsic property of fast streams, while slow intervals typically have a very low degree of Alfvénicity, with much more variable parameters. However, sometimes a slow wind can be highly Alfvénic. Here we compare three different regimes of solar wind, in terms of Alfvénic content and spectral properties, during a minimum phase of the solar activity and at 0.3 au. We show that fast and Alfvénic slow intervals share some common characteristics. This would suggest a similar solar origin, with the latter coming from over-expanded magnetic field lines, in agreement with observations at 1 au and at the maximum of the solar cycle. Due to the Alfvénic nature of the fluctuations in both fast and Alfvénic slow winds, we observe a well-defined correlation between the flow speed and the angle between magnetic field vector and radial direction. The high level of Alfvénicity is also responsible of intermittent enhancements (i.e. spikes), in plasma speed. Moreover, only for the Alfvénic intervals do we observe a break between the inertial range and large scales, on about the timescale typical of the Alfvénic fluctuations and where the magnetic fluctuations saturate, limited by the magnitude of the local magnetic field. In agreement with this, we recover a characteristic low-frequency 1/f scaling, as expected for fluctuations that are scale-independent. This work is directly relevant for the next solar missions, Parker Solar Probe and Solar Orbiter. One of the goals of these two missions is to study the origin and evolution of slow solar wind. In particular, Parker Solar Probe will give information about the Alfvénic slow wind in the unexplored region much closer to the Sun and Solar Orbiter will allow us to connect the observed physics to the source of the plasma.