Bengali Year starts in April. For Bangladesh it is always 14th of April. On the other hand in India it is celebrated on 14th or 15th of April. Also , in other Bengali months we often observe difference in Bengali Date . Why there is a difference in Dates in Bangladesh and India? Of course both are Bengali date, Month names are also same!
To answer this question we would have to turn back and look at the origin. But the History on this subject is not clear and there are different theories on the origin of Bengali Calendar. But all of them agree that Mughal Emperor, Akbar is the key person in Promoting the Bengali Calendar. It was done to make the tax collection easy for the farmers. The lunar Islamic Calendar is based on moon and does not go along with the seasons. At times this caused farmers to pay tax out of season. In order to solve this problem Lunisolar Bengali Calendar was formed.
But this Calendar is not consistent with month lengths. Number of days in a month can vary from 29 to 32. The Bengali calendar in Bangladesh was modified by a committee headed by Muhammad Shahidullah under the auspices of the Bangla Academy on 17 February 1966. The same was officially adopted by the Bangladesh Government in 1987. According to this Calendar the first five months of a Bengali year consists of 31 days. And the next 6 months would have 30 days each. Thus a year consists of 365 days. Which is same with Gregorian or English Calendar. And for a leap year the month of Falgun will have 31 days adding the value to 366.
So Bengali Calendar in Bangladesh is quite straightforward. Whereas in India people still follows the old one. Thus we observe a difference in dates between Bengali Calendar used in India and Bangladesh.