Hello Sir,
1 year mba program is for working professional executives only. It is of a duration of 1 year or 15 months offered by some prominent institutes in India. Rest every where you'll be offered 2 year mba or pgdm.
MBA is offered by universities and PGDM is offered by autonomous institutes but PGDM should be a valid and certified by AIU (THE ASSOCIATION OF INDIAN UNIVERSITIES) and acceoted by AICTE and UGC. Institutes like IIM's also offer pgdm. PGDM should be equivalent to mba and it should be of 2 years.
A valid pgdm or mba is acceptable for government jobs in India.

Answer to the second part of your question:
Yes you can pursue Phd after completing your MBA or PGDM but the either of the course should be valid and holds value.

I hope this information helps you and clarifies your doubts.

All the best !!

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