Why do we hoist flag on Independence Day but unfurled on Republic Day?

On Independence Day, the Tricolour is fastened to the lowest section of the flagpole and raised by the Prime Minister. 

This act represents the country's emancipation from colonial domination.

On Republic Day, the flag is knotted at the top and then unfurled.

This signifies the development of new ideas and laws, as well as a reinvigorated devotion to the Indian Constitution.

The word hoist means to raise something using ropes and pulleys.

Unfurling means to make or become spread out from a rolled or folded state, particularly to expose to the wind.