There are actually two schools or groups which make the Hindu Panchangams or almanacs .They are called the Panchangam Kartaa.
One among them use the old school method depending on the Surya Siddhanta(or Vakya Siddhanta) and another one depends on the Drik Ganita ,which uses modern methods to calculate the positions of the stars.Their calculations match with those of say the Nasa Ephemeris.
The Panchangam or calender,called the "Rashtriya Panchanga", which is published by the Indian Government also supports the Drik Ganita method and not that based on the Surya Siddhanta.
The difference that you see between the two calendars is due to the fact that both uses different algorithms to calculate the star positions.
Needless to say,the Surya Siddhanta method gives erroneous results where as the Drik Ganita method gives precise and correct results.
One group of Panchangam makers uses old methods which were quite handy
to give correct positions of stars without doing lengthy calculations.
Old calculations were written in form of statements or Vakya for easy
memorization and understanding. Those shortcuts used to get updated
time to time to remove any inaccuracies which creeps in such methods
with time. The calculated positions of stars by Vakyam and Surya
Siddhantic methods were exact enough to match with observatory
positions of the stars without much effort.
These old methods have not been updated since centuries and star
positions calculated by these methods are erroneous. The difference
between calculated and observatory positions might vary up to 12
hours. Hence the positions of star calculated by old algorithms like
Vakya Siddhanta or Surya Siddhanta are not precise. Followers of these
old schools are well aware of these discrepancies but still use
erroneous methods. However they don't mind stealing eclipse
information from Drik Panchangam or Thiru-Ganita Panchangam.
Many Tamil and Bengali Panchangams still use the Surya Siddhanta.whereas both the Raman Ephemeris and the Drikpanchang use the Drika Ganita.Its better to rely on them.
I personally always use the Drikpanchang.com website.