We have measured forces between surfaces with controlled "hydrophobicity" in pure water, where the outermost atomic layer of the surfaces is composed of both CH3CH2- and HOCH2- groups. We have demonstrated that the so-called long-range attraction that acts between macroscopic hydrophobic surfaces across water comprises (at least) two force components of considerably different character with respect to its dependence on the "hydrophobicity" of the surface. In a longer distance regime (D > 15-20 nm), there is no one-to-one correlation between the range and magnitude of the attraction and the "hydrophobicity" of the surfaces as defined by the interfacial free energies with water, gamma(sL), or the water contact angles, theta(a). Hence, the attraction in a longer distance regime is not directly related to "hydrophobic interactions". In a shorter distance regime (D < 5-20 nm, the range depends on the surfaces concerned), the surfaces experience a very rapidly increasing attraction that is not solely a van der Waals force in origin. The energy of interaction in this regime is largely due to large positive values of the interfacial free energy of the surfaces, an indication that the attraction in the shorter distance regime reflects "hydrophobic interaction". Owing to experimental difficulties, we could only estimate an upper bound for the range of interactions; a range of "hydrophobic interaction" between macroscopic hydrophobic surfaces across water is at most 15-20 nm, Present results strongly suggest that the longer-range and the shorter-range part of the attraction have their origin in distinct molecular mechanisms.