What is the difference between natural draft, power vent, and direct vent products?
When discussing fuel cost as it pertains to venting and combustion, two things that affect fuel efficiency are how much air is needed for venting and maintaining water temperature. The draft type of the appliance is important, and no new heating appliance in a residential application should stay hot all the time, except for a boiler with a domestic hot water coil. Boilers with internal coils should not be considered in new appliances. The reason is that this is the most expensive method for producing hot water using new equipment. You can use an indirect water heater connected to the boiler, and the boiler would still be of a cold start configuration.
Natural Draft (Least efficient)
Natural draft is a connection to a chimney. The chimney will draft all products of the combustion process. Unfortunately, it will vent constantly. When the heating appliance is running, it needs to vent its byproducts. However, when it shuts down, the chimney continues to vent as it cools down. The lower the internal chimney temperature, the lower the draft. The biggest downside of a chimney is that it is always drafting. This drafting process is stealing heat from the home 24 hours a day, 7 days a week. It will actually increase the heat loss. As the air is moving up the chimney as a draft, it must be replaced through air leaks in the home. When the heating appliance fires, it requires even more air to be pulled into the home, thus increasing heat loss. See heat loss or heat loss FAQ. The use of vent dampers on gas appliances will assist with, but not avoid, off-cycle losses. All the air for draft and combustion must be replaced with fresh air. If the home is tight and we do not get enough fresh air pulled into the home, we have combustion issues such as Carbon Monoxide (CO).
Many products have been, and still are, sold as chimney-vented products. The good thing is that these products have a cold start, which means the boilers do not have to maintain a constant water temperature all the time. The only equipment that maintains water temperature is a boiler equipped with a domestic hot water coil. This is old school and a waste of energy. Please avoid domestic water coils in boilers at all times, and this alone will start saving fuel.
Power Vented Products (Medium Efficient)
Power venting means using a fan for drafting the products of combustion either through the side wall or roof. The air for combustion is received from inside the home, but no draft is required. This will cause less air to be brought into the home through cracks and crevices. It is still removing warm heated air, and that air is being replaced with cold air. We could still experience the same CO issues as above. None of these products should maintain water temperature.
Drawing of power vented boiler
Direct Vent Products 
(Most Efficient)
Direct vented products are similar to power vent products, with the exception that they will pull all the combustion air from the outside. This, combined with no chimney draft, will reduce heat loss, as no air from inside the structure will be used during the combustion or venting process. This will assist in fuel savings and increased comfort. None of these products should maintain water temperature.
When talking about direct venting, it can be done as a two-pipe system, one being the vent and the other being the fresh air intake. There is a second option for direct venting, which is a concentric vent. The concentric vent is one penetration. The hole through the wall or ceiling is a little larger, but the concentric pipe is a pipe in a pipe. The outer pipe serves as the air intake, and the smaller inner pipe functions as the vent.
Drawing of direct vent boiler.
Also see terminations of sealed combustion two pipe and Concentric . The terminations vary slightly among manufacturers.
