An effective methodology for the detailed analysis of thermal desorption spectra (TDS) of hydrogen in carbon structures at micro- and nanoscale was further developed and applied for a number of TDS data of one heating rate, in particular, for graphite materials irradiated with atomic hydrogen. The technique is based on a preliminary description of hydrogen desorption spectra by symmetric Gaussians with their special processing in the approximation of the first- and the second-order reactions. As a result, the activation energies and the pre-exponential factors of the rate constants of the hydrogen desorption processes are determined, analyzed and interpreted. Some final verification of the results was completed using methods of numerical simulation of thermal desorption peaks (non-Gaussians) corresponding to the first- and the second-order reactions. The main research finding of this work is a further refinement and/or disclosure of poorly studied characteristics and physics of various states of hydrogen in microscale graphite structures after irradiation with atomic hydrogen, and comparison with the related results for nanoscale carbon structures. This is important for understanding the behavior and relationship of hydrogen in a number of cases of high energy carbon-based materials and nanomaterials.