You are absolutely correct Faiz. After the most unfortunate partition of Bengal the people of two parts have developed two different identities.
People from WB have an Indian identity, accepting and respecting Bangla as their mother tongue and accepting and assimilatin other languages, food habit, attires, life style. So it's a beautiful uniqueness amidst diversity. That's Indian.
If Bengal had not been partitioned on religious grounds, the united Bengal would have had the same Indian identity.
But Bangladesh has chosen religion above all along with the language. It's different from WB.