Context. The properties of a solar wind stream are determined by its source region and by transport effects. Independently of the solar wind type, the solar wind measured in situ is always affected by both. This means that reliably determining the solar wind type from in situ observations is useful for the analysis of its solar origin and its evolution during the travel time to the spacecraft that observes the solar wind. In addition, the solar wind type also influences the interaction of the solar wind with other plasma such as Earth’s magnetosphere. Aims. We consider the proton-proton collisional age as an ordering parameter for the solar wind at 1 AU and explore its relation to the solar wind classification scheme developed by Xu & Borovsky (2015, J. Geophys. Res.: Space Phys., 120, 70). We use this to show that explicit magnetic field information is not required for this solar wind classification. Furthermore, we illustrate that solar wind classification schemes that rely on threshold values of solar wind parameters should depend on the phase in the solar activity cycle since the respective parameters change with the solar activity cycle. Methods. The categorization of the solar wind following Xu & Borovsky (2015, J. Geophys. Res.: Space Phys., 120, 70) was taken as our reference for determining the solar wind type. Based on the observation that the three basic solar wind types from this categorization cover different regimes in terms of proton-proton collisional age acol, p-p, we propose a simplified solar wind classification scheme that is only based on the proton-proton collisional age. We call the resulting method the PAC solar wind classifier. For this purpose, we derive time-dependent threshold values in the proton-proton collisional age for two variants of the proposed PAC scheme: (1) similarity-PAC is based on the similarity to the full Xu & Borovsky (2015, J. Geophys. Res.: Space Phys., 120, 70) scheme, and (2) distribution-PAC is based directly on the distribution of the proton-proton collisional age. Results. The proposed simplified solar wind categorization scheme based on the proton-proton collisional age represents an equivalent alternative to the full Xu & Borovsky (2015, J. Geophys. Res.: Space Phys., 120, 70) solar wind classification scheme and leads to a classification that is very similar to the full Xu & Borovsky (2015, J. Geophys. Res.: Space Phys., 120, 70) scheme. The proposed PAC solar wind categorization separates coronal hole wind from helmet-streamer plasma as well as helmet-streamer plasma (slow solar wind without a current sheet crossing) from sector-reversal plasma (slow solar wind with a current sheet crossing). Unlike the full Xu & Borovsky (2015, J. Geophys. Res.: Space Phys., 120, 70) scheme, PAC does not require information on the magnetic field as input. Conclusions. The solar wind is well ordered by the proton-proton collisional age. This implies underlying intrinsic relationships between the plasma properties, in particular, proton temperature and magnetic field strength in each plasma regime. We argue that sector-reversal plasma is a combination of particularly slow and dense solar wind and most stream interaction boundaries. Most solar wind parameters (e.g., the magnetic field strength, B, and the oxygen charge state ratio no7+/no6+) change with the solar activity cycle. Thus, all solar wind categorization schemes based on threshold values need to be adapted to the solar activity cycle as well. Because it does not require magnetic field information but only proton plasma measurements, the proposed PAC solar wind classifier can be applied directly to solar wind data from the Solar and Heliospheric Observatoty (SOHO), which is not equipped with a magnetometer.