A hard reboot will involve having a physical person at the router location and toggle it off and on.
A reboot will terminate all sessions, reset the hardware, load and verify the software image, execute system diagnostics, and initialize the system.
A reload will involve remotely re-initializing the router/equipment. Reload will deny access to the router/equipment, and connectivity is interrupted briefly between the switches/routers and end stations.
I hope this helps a little.
Emil.