what is the difference between hotel management and hospitality management??

Hotel Management is part of the Hospitality Industry, where the entire organization, output and processes of the organization are exposed to the public and evaluated/judged by the public. Working the hospitality industry requires being constantly mindful and accommodating to the needs of the public

The second one has a broader field, as I feel.

Hotel mamnagement is running a hotel and hospitality is the term used for an industry based on hospitality(dealing with people) - Hotel, restaurant, pub, night clubs, travel agents etc. So hotel management is part of the hospitality industry.