Ships DO have doors. Not every opening on a ship is a hatch. They also can have stairs. The general definition of a door vs a hatch on a ship depends an the direction they give access. The opening between compartments are generally doors. That is why you hear the phrase “Water tight Doors” or "Dog the water tight doors". If you pass through the opening horizontally, if is usually a door. The exception to this is if the opening is higher up than a person can simply step through. If you have to climb up to the opening, it is generally a hatch. And the opening between levels is definitely, always, a hatch. So the Captains Ready Room (and yes ships also have rooms) has a door; not a hatch. Also the difference between a ladder and a stair is the angle. As the stair becomes steeper, it becomes a ladder. The aircraft carriers I served on had stairs between the hangar deck and the flight deck. OSHA says anything more than 50 degrees from horizontal is a ladder. Most ships cannot afford the space that is needed for stairs. So they install ladders instead. But between the flight deck and the hangar deck, there was plenty of room for stairs and that is what we had. Most were escalators (that never worked).
In the EDF, a 'hatch' is doorway that can be sealed. (As in airtight.) Doors cannot be sealed. (There are no 'airtight doors'.) The captain's ready room has a hatch because it is designed to be an emergency airlock. (There is a tunnel in the back corner that leads to a rescue hatch topside.)
Always remember, this isn't the Navy. It's 1400 years later. There ain't no 'poop deck' either.
I think it is fair to say that to the layman, a hatch is a door is a hatch, but definitively not a stairs.