Context. The star S CrA is a tight visual binary consisting of two classical T Tauri stars. Both components are outstanding regarding their spectral characteristics and brightness variations. Aims. Our aim is to explore the extraordinary spectral features seen in these stars, derive stellar parameters, define spectral signatures of accreting gas and winds, estimate the inclinations of the disks, and to match numerical models with observed properties. Methods. High-resolution spectra were collected of each component over several nights at the European Southern Observatory (ESO) combined with photometric observations covering several years in UBVRI with the SMARTS telescope. The models developed include magnetospheric accretion and a disk wind. Results. Both stars undergo large variation in brightness, ≥2 mag in V band. The variations are caused mainly by variable foreground extinction from small-size dust grains, which may be carried along with the accreting gas. The photospheric absorption lines are washed out by superimposed continuous and line emission, and this veiling becomes occasionally exceptionally high. Nevertheless, we extracted the stellar spectra and found that both stars are very similar with regard to stellar parameters (T_eff, log g, v sin i, mass, radius, luminosity). The rotational periods, inferred from velocity shifts in lines originating in surface areas off-set from the pole, are also similar. Combined with the v sin i:s related inclinations were obtained, which agree well with those derived from our model simulations of Balmer line profiles: ∼65° for both stars. At this orientation the trajectories of infalling gas just above the stellar surfaces are parallel to the line-of-sight, and accordingly we observe extended red-shifted absorption components extending to +380 km s^-1, the estimated free-fall velocity at the surface. Rates of accretion and mass loss were obtained from the models. Conclusions. The two stars are remarkably similar, and S CrA can be regarded as a T Tauri twin. The components differ, however, in terms of degree of veiling and emission line profiles. We have found a good match between observed signatures of accreting gas, wind features, and rotational velocities with those resulting from our modelling for inclinations of ~65?. These inclinations differ from those derived from interferometric near-infrared (NIR) spectroscopy, and possible causes for this puzzling discrepancy are discussed.