Need some help on defining this because there are some different interpretations of how this works. I am confused.

Does a ship in port count as a unit in an army that is occupying the adjacent land area connected to the port?

All Units are Baratheon

For example: Dragonstone has 2 footmen, the port on Dragonstone has 1 ship. Does this make an army of 3?

OR

Are the 2 units in Dragonstone considered an army of 2, meanwhile the ship in port is merely just 1 unit in port.

No, the ship in port does not count as an army with the adjacent land area.

The second one.

In the case described, you have an army of 2 in Dragonstone and an 'army' of 1 in Dragonstone Port.