Reset usually means setting the router back to its initial factory settings that are very basic and not secure. E.g., login name is "admin", password is "password", etc. Network name may be the name of the manufacturer. Most such default settings are listed in the user guide/manual.
Restore means that a router has been all customized for its intended network use and the user/admin person has modified some or all the various factory settings to meet the network requirements. Quality of Service, white-lists, wireless channels, passwords, SSID for example.
Once those customized settings are complete they can be saved. If some future router modification goes astray or something else happens the saved copy of the customized...