Which course is better in terms of career prospects and placements: MBA or MBM? Can you share complete details regarding IB?

Your question is incorrect you are confused between MBA and MBA NMIMS college and MBA is degree.

Organisations do not see nomenclature of your degree whether it is PGPM, PGDM, MBM, MMS or MBA. What matter is the reputation of the institute, your own personal quality and how you convince your recruiter. For IB related thing, check with your institute. IIFT is one of such very valuable institute.