Based on the stellar orbit distribution derived from orbit-superposition Schwarzschild models, we decompose each of 250 representative present-day galaxies into four orbital components: cold with strong rotation, warm with weak rotation, hot with dominant random motion, and counter-rotating (CR). We rebuild the surface brightness (Σ) of each orbital component and we present in figures and tables a quantification of their morphologies using the Sersic index n, concentration C = log {(Σ _{0.1R_e}/Σ _{R_e})} and intrinsic flattening qRe and qRmax, with Re the half-light radius and Rmax the CALIFA data coverage. We find that: (1) kinematic hotter components are generally more concentrated and rounder than colder components, and (2) all components become more concentrated and thicker/rounder in more massive galaxies; they change from disc-like in low-mass late-type galaxies to bulge-like in high-mass early type galaxies. Our findings suggest that Sersic n is not a good discriminator between rotating bulges and non-rotating bulges. The luminosity fraction of cold orbits fcold is well correlated with the photometrically decomposed disc fractiondisc f_disc as f_{cold} = 0.14 + 0.23f_{disc}. Similarly, the hot orbit fraction fhot is correlated with the bulge fraction fbulge as f_{hot} = 0.19 + 0.31f_{bulge}. The warm orbits mainly contribute to discs in low-mass late-type galaxies, and to bulges in high-mass early-type galaxies. The cold, warm, and hot components generally follow the same morphology (ɛ = 1 - qRmax) versus kinematics (σ _z^2/\overline{V_{tot}^2}) relation as the thin disc, thick disc/pseudo-bulge, and classical bulge identified from cosmological simulations.