If you're on a boat in open water during the middle of a storm, the last thing you want to be worrying about is whether or not your doors will be able to keep the water out. But depending on what type of doors you have, they could be a source of major concern. The biggest difference between weather tight doors and watertight doors is what direction the water is prevented from flowing. In the case of weather tight doors, water won't come in from the outside, but can go from the inside out. Watertight doors keep water from flowing in both directions.
Weather Tight Doors
Designed for short term submersion at most, doors that are classified as being "weather tight" are usually on the top level of a boat, above the surface of the water. They're less expensive than their watertight counterparts, mainly because they only are rated to protect against water pressure from one direction. As the water rushes in, it pushes weather tight doors back against a seal and prevents any kind of water from flowing through, which is especially handy in the case of a storm. Once the water stops pressing against the door, the door relaxes and water is able to escape back outside, which prevents flooding on the exterior.
Watertight doors, on the other hand, are able to withstand water from both directions and are usually kept below the surface of the water. In the event of a break in one area, water will be confined to a certain location and won't spread to various other parts of the vessel, keeping it afloat. This is not a one-size-fits-all solution, as watertight doors are generally classified by varying degrees of protection - either for longer periods of submersion or against more direct water.
Which One Do I Need?
Since you'll probably need more weather tight doors that you do watertight, those are generally less expensive, but how many you need depends on the size of your boat. It also depends on how prolonged of a voyage you plan on using your boat for, and what type of water you find yourself in. If you plan on sailing for days or even weeks at a time, you'll need more watertight doors on the interior of the cabin to prevent water from moving around in the event of an accident. Weather tight doors on the top part of the boat should provide protection against moderately sized waves, but if your doors are older, have them replaced before going too far off shore.