The enhanced large‐scale model and numerical simulations are used to clarify the growth mechanism and the differences between the plasma‐ and neutral gas‐grown carbon nanotubes, and to reveal the underlying physics and the key growth parameters. The results show that the nanotubes grown by plasma can be longer due to the effects of hydrocarbon ions with velocities aligned with the nanotubes. We show that the low‐temperature growth is possible when the hydrocarbon ion flux dominates over fluxes of other species. We have also analysed the dependencies of the nanotube growth rates on nanotube and process parameters. The results are verified by a direct comparison with the experimental data. The model is generic and can be used for other types of carbon nanostructures such as carbon nanowalls, vertical graphenes, etc.