ABSTRACT Motivated by the recently discovered kinematic ‘Hubble sequence’ shown by the stellar orbit-circularity distribution of 260 CALIFA galaxies, we make use of a comparable galaxy sample at z = 0 with a stellar mass range of $M_{*}/\mathrm{M}_{⊙ }𝟄 [10^{9.7},\, 10^{11.4}]$ selected from the IllustrisTNG simulation and study their stellar orbit compositions in relation to a number of other fundamental galaxy properties. We find that the TNG100 simulation broadly reproduces the observed fractions of different orbital components and their stellar mass dependences. In particular, the mean mass dependences of the luminosity fractions for the kinematically warm and hot orbits are well reproduced within model uncertainties of the observed galaxies. The simulation also largely reproduces the observed peak and trough features at $M_{*}≈ 1\rm {-}2\times 10^{10}\, \mathrm{M}_{⊙ }$ in the mean distributions of the cold- and hot-orbit fractions, respectively, indicating fewer cooler orbits and more hotter orbits in both more- and less-massive galaxies beyond such a mass range. Several marginal disagreements are seen between the simulation and observations: the average cold-orbit (counter-rotating) fractions of the simulated galaxies below (above) $M_{*}≈ 6\times 10^{10}\, \mathrm{M}_{⊙ }$ are systematically higher than the observational data by $\lesssim 10{{\ \rm per\ cent}}$ (absolute orbital fraction); the simulation also seems to produce more scatter for the cold-orbit fraction and less so for the non-cold orbits at any given galaxy mass. Possible causes that stem from the adopted heating mechanisms are discussed.