Public holiday is a holiday which is observed in a public office and includes a national holiday. In government sector there is no such national holiday but they have closed holidays and restricted holidays. The former are the days on which the office will remain closed and the latter are the days on which the office will be open but some of the employees will enjoy holiday. Since the government offices are meant for the general public ( even though the employees sitting there feel that the office is just for their enjoyment and a source of revenue to them) and as such the government has an obligation to inform the public that the office will remain closed on certain days and hence these holidays are called public holidays.
Coming to national Holidays, it is an outcome of a thought that the private establishments if not put any restriction with regard to closing on certain days will run all the days without giving the employees any holiday to enjoy. Therefore,various state governments made their own Acts and rules concerning holidays. While deciding which all are the days on which the establishment should be closed the main thing which came in to thought were that there should be some common days which are of national importance which all the establishments should observe as holiday and these are called National Holidays. Again this is left to the discretion of the state. Almost all states have declared three days as holidays of national importance and they are January 26th, August 15th and October 2nd. At the same time many states have included May 1st being international labour day as national Holiday and Karnataka has included one more day, November 1st, their state formation day as a holiday which should be observed by all establishments. Since these are mandatory holidays which are not connected with any festival or religious faith or sentiments, these are called national Holidays.
When we find the difference between Public Holidays, we can see that all national Holidays are Public Holidays but all public holidays are not National Holidays. For example, Christmas is a Public Holiday but it is not a national holiday because it is connected with a religious faith.