We used the new IRAM 30-m FTS backend to perform an unbiased ~15 GHz wide survey at 3 mm toward the Pipe Nebula young diffuse starless cores. We found an unexpectedly rich chemistry. We propose a new observational classification based on the 3 mm molecular line emission normalized by the core visual extinction (Av). Based on this classification, we report a clear differentiation in terms of chemical composition and of line emission properties, which served to define three molecular core groups. The diffuse cores, Av<~15, show poor chemistry with mainly simple species (e.g. CS and CCH). The oxo-sulfurated cores, Av~15--22, appear to be abundant in species like SO and SO2, but also in HCO, which seem to disappear at higher densities. Finally, the deuterated cores, Av>~22, show typical evolved chemistry prior to the onset of the star formation process, with nitrogenated and deuterated species, as well as carbon chain molecules. Based on these categories, one of the diffuse cores (Core 47) has the spectral line properties of the oxo-sulfurated ones, which suggests that it is a possible failed core.