I wonder if usage in India was influenced by the British. They evidently didn't build the forts, but did they perhaps take existing buildings and turn them into forts, in the sense of military encampments?
To me military occupation is a typical context for a fort as opposed to a castle; you build a castle if you live there and own the land as a wealthy and powerful individual, and perhaps have some knights who owe you fealty and can help you defend what is yours. But you build a fort if you come in with an army, want to govern the land, and expect resistance from the people who are already there. (And if you expect a siege, you make the fort a fortress, that is, more heavily built and fortified, difficult or impossible to penetrate.)
Another distinction might be that a fort in the historical sense was typically built less permanently, i.e., with logs more than with stone and mortar. I'm thinking here of Celtic hill forts, or early US forts in the days of the Indian wars. And a modern fort isn't a single building, it's a large military encampment.