Anna some of the top universities of Chennai from where you can do your part-time MBA in HR are:

• Suresh Gyan Vihar University Distance Education, Talentedge, Chennai 
• Indian Institute of Business Management and Studies, T Nagar, Chennai
• Great Lakes Institute of Management, Chennai, Kanchipuram, Chennai
• Loyola Institute of Business Administration, Nungambakkam, Chennai 
• EINS Education, Welingkar Institute of Management, Anna Nagar, Chennai 
• Anna University, Guindy, Chennai
• NMIMS Global Access School for Continuing Education, NMIMS University, Guindy, Chennai
• School of Distance Education and Learning (Online), Jaipur National University, Anna Nagar, Chennai
• SRM University, Vadapalani Campus, Chennai
• Indian Institute of Knowledge Management, Chennai

MBA HR stands for Masters in Business Administration Human Resources and MHRM stands for Masters in Human Resource Management. 

Both are almost similar courses that are offered by various universities and B Schools in India and International Universities. Both teach the various aspects of Human Resource Management and constitutes a set of core courses as well as specializations electives as per your interest.

MHRM is offered in TISS. You will learn a lot of role of HR in Social Context. You have good scope to work in CSR works. MBA in HR will teach you to learn things which are useful for daily HR works like recruitment/talent acquisition, payroll etc.

In your context, I think MBA in HR will be better but still, I will highly recommend you to go through the course structure of whichever college you are joining as different institutes have different strengths and legacy of teaching the courses. This will also help you in identifying the best college and course for yourself.

Feel free to ask if you have any more queries. All the best!!