HR (HRD) - Human Resources Department. It is responsible for the staff (employee) management in an organisation. Example responsibilities: Recruiting, Lay-offs, Pay-Packets etc.
PR (PRM) - Public Relations Management. It comprises of all activities done to keep the public involved in the company. PR used to be the 'point of contact' between the (general) public (esp. Media) and the organisation. However, modern PR has donned a more of marketing role. For example, most celebrities hire PR fellows who in turn (through their contacts) get them published in various media, arrange for entry in privileged parties, sustaining a large public interest in them through various means (including fabricating controversies :P ) etc.