I think Personnel Management and HR Management are almost the same because both are related to the employees of the concern. Maybe the difference lies where Personnel Management deals with the management of each employee, like their personal attitude, grievances, motivation, etc., and HR Management encompasses Personnel Management along with everything else relating to the employee, such as salary, leaves, training, and development of employees.
However, it is in no way connected to Admin (arrange/manage for establishment). Admin Management is a different thing altogether, where the admin person is responsible for all the office-related work like maintaining stationery, obtaining requirements, negotiating price, quality, and delivery, approving invoices, etc.
Regards