We study angular and frequency-angular distributions of the terahertz (THz) emission of the low-frequency region (0.3-3 THz) from a two-color femtosecond plasma spark experimentally and in three-dimensional numerical simulations. We investigate the dependence of the angular shapes of the THz radiation on focusing conditions and pulse durations by using two laser facilities (pulse durations 35 and 150 fs) for different focusing geometries. Our experiments and simulations show that decrease in the numerical aperture from NA ≈0.2 to NA ≈0.02 results simultaneously in (I) squeezing of the THz angular distribution and (II) formation of the bright conical emission in the THz range. The moderate focusing NA ≈0.05, which forms the relatively narrow unimodal THz angular distribution, is identified as optimal in terms of angular divergence. Numerical simulations with carrier wave resolved show that bright THz ring structures appear at the frequencies ≥2 THz for longer focuses (NA ≈0.02), while for optimal focusing conditions NA ≈0.05 the conical emission develops at THz frequencies higher than 10 THz.