General HR Question:

Usually these two terms are used interchangeably but there does lie a difference between the two.

Personnel management is reactive in nature and includes administrative tasks while HRM is proactive in nature and requires continous develpment in policies and functions of the organization for a better tomorrow.
Personnel management is more of an independent task than HRM which needs to involve the managers of all departments for developing a better team.
Personnel mangement believes that satisfied employees yield better performance while HRM believes that a good performance provides satisfaction to employees.
HRM works around developing startegies to improve the performance of employees. Personnel mangement works around motivating employees with compensation, bonuses, rewards etc.
Actually Personnel management can be considered as a subset of HRM.
Here you have to bear in mind that if you are offered the position of a Personnel Manager, you may be required to perform HRM functions and vice versa.