Aims. In the framework of the GIARPS@TNG High-resolution Observations of T Tauri stars (GHOsT) project, we study the accretion properties of 37 Classical T Tauri Stars of the Taurus-Auriga star forming region (SFR) with the aim of characterizing their relation with the properties of the central star, of jets and disk winds, and of the global disk structure, in synergy with complementary ALMA millimiter observations. Methods. We derive stellar parameters, optical veiling, accretion luminosity (L acc ) and mass accretion rate ( Ṁacc ) in a homogeneous and self-consistent way using high-resolution spectra acquired at the Telescopio Nazionale Galileo with the HARPS-N and GIANO spectrographs, and flux-calibrated based on contemporaneous low-resolution spectroscopic and photometric ancillary observations. Results. The L acc -L , Ṁacc -M and Ṁacc -M disk relationships of the Taurus sample are provided and compared with those of the coeval SFRs of Lupus and Chamaeleon I. We analysed possible causes giving rise to the observed large spreads in the relationships. We find that: (i) a proper modeling in deriving the stellar properties in heavily spotted stars can reduce the spread of the Ṁacc -M relation, (ii) transitional disks tend to have lower Ṁacc at a given M , (iii) stars in multiple systems have higher Ṁacc at the same M disk , (iv) the Ṁacc vs the disk surface density has a smaller spread compared to that of the Ṁacc -M disk , indicating that opacity effects might be important in the derivation of M disk . Finally, the luminosities of the [O i] 630 nm narrow-low-velocity component (NLVC) and high-velocity component (HVC) and the de-projected HVC peak velocity were found to correlate with the accretion luminosity. We discuss such correlations in the framework of the currently accepted jets/winds models. Conclusions. Our results demonstrate the potential of contemporaneous optical and near-infrared high-resolution spectroscopy to simultaneously provide precise measurements of stellar and accretion/wind properties of young stars.