What are the college's that offer the master's in healthcare administration ?

The best colleges for healthcare administration are as follows:
Tata Institute of Social Sciences, Mumbai
IIHMR, Jaipur
IIHMR, Delhi, Bangalore and Kolkata.
ASCI, Hyderabad
NMIMS for pharmaceutical management.

Is there a difference between healthcare administration and hospital management course ?

Yes, there is a difference.
The first year of training is the same for both the courses at institutes like IIHMR and depending on your choice and marks, you can choose a field in second year. Then onwards the curriculum and the internships differ.
Also, I would like to say that globally, healthcare administration is better accepted.

I am in the final year of my graduation in biochemistry so can I apply for master's in healthcare administration in these institutes ?

Yes you can. Eligibility criteria is slightly different from college to college but 50 % and above in your graduation is basic eligibility. There is separate entrance exam for Tiss called Tissnet and IIHMR accepts the score of MAT.
You will have to justify your decision of switching over from biochemistry to healthcare in interviews, also some experience in the field of healthcare improves your cv.
By and large, your colleagues will be from dentistry background but in the field of healthcare, they are considered almost equal to you as dental experience has nothing to do with the way healthcare industry operates. The only hurdle is MBBS colleagues which will always be considered superior to you, irrespective of your experience or position. You must consider all these factors before hand.
Healthcare administration will be a good option for you but avoid hospitals as they prefer MBBS background and thus hospital administration should not be on your cards.

Around what month the forms are usually out for these examinations and how do I prepare for these exams so that I can perform good ?

As you recommended IIHMR Jaipur so I checked its site but they are offering master's of hospital and health Care Management and I wish to do master's in healthcare administration so are these same ?

Once you get admitted to the course, the first year of hospital and healthcare administration is same but in second year you get an option of hospital or healthcare, after which your course changes depending on your choice.