What is the major difference between the freely available CartoDEM from Bhuvan web portal and CartoDEM of ortho image resolution 2.5m which is to be procured from NRSC if needed?
I think the DEM products that can be ordered from NRSC have the possibility for ortho rectification, that's why the name ortho image, whereas the ones available freely from Bhuvan are only radiometrically corrected and georeferenced. Check the Brochure link for more info.
The CartoDEM and ortho image were generated using CartoSat-1 Stereo pairs (or Stereo Images) by National Remote Sensing Centre (NRSC), Hyderabad. The resolution of CartoSat-1 Stereo pair is 2.5 m. Therefore, the resolution of Ortho image is 2.5m and DEM is 10m. But DEM available in Bhuvan is 30m (The 10m DEM resembled in to 30m). If you want 10m DEM, you have to procured CartoSat-1 Stereo pairs from NRSC and generate DEM and ortho image. All the best.