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I know that one of the best ways to save energy at home is insulation. The question is, is there a different method for keeping the heat in when it's cold and keeping the heat out when it's warm?
I know that there is a lot to be done with shade/sunlight and such, but this question is specifically about insulation materials and methods.
In reality, yes, it probably does matter. In each case, it will depend on a lot of detail, so I'll discuss the theoretical concepts, rather than any one particular application.
Heat moves about through a combination of three ways. One, two or all three might be significant in any particular case.
convection - the movement of hot air to a colder place, and the movement of cold air to a hotter place.
radiation - the transfer of heat through electromagnetic radiation, such as the sun shining in.
conduction - the passage of heat through a material.
Thermal mass, or thermal inertia, represents a heat store. It is, in the broadest sense, the sum of mass x specific heat of everything in the house. Air has a very low thermal mass; concrete, bricks, plaster, have much higher thermal masses. If you use internal wall insulation, your rooms will have lower thermal mass. If you use external wall insulation, your rooms will have higher thermal mass. Higher thermal mass means more temperature stability - you have to move a lot more energy to change their temperature by a given number of degrees Celsius.
Buildings that are too cold, are typically losing a lot of heat through convection and conduction. To fix this, insulation should increase air-tightness, to reduce convection, and should add thermal resistance, reducing conduction.
Buildings that are too hot, are typically gaining a lot of heat through direct solar radiation. In this case, preventing sunlight coming into the building at all is the first priority; next, prevent sunlight falling on walls that are directly connected to the inside of the property, and get as much air through the property as possible, when temperatures drop at night - this is also called night purge ventilation
One related difference between keeping heat in or out relates to the climate - it's temperature and humidity.
The reason for needing a vapor barrier is that when air passes through the insulation from the warm side to the cool side, it is cooling. As the temperature drops through the insulation, some of the water vapor will condense causing the insulation to be wet. Fiber glass insulation that is wet does not insulate as well as dry insulation as the water helps to conduct heat through the insulation. To make matters worse, the wetness can then reach the cool wall and water condensation can now form on that wall leading it to rot due to bacteria growing in the now damp environment.
There is no difference in the insulative materials, but there a different in their placement relative to the heat source.
This is why in most parts of the US, and in southern Europe, well constructed homes have a foil facing underneath the siding, followed by a thin phenolic (often these first two steps are integrated into one rigid foam board), then the framing interlaced with fiberglass/cellulose/spray foam.
For a thermos flask, insulation will both keep in cold and keep out warm & keep out cold and keep in warm.
A house is different, because it has windows. Sunlight is warmth that can pass through windows. So, to keep your house warm, you should have windows that let in enough sunlight and make sure that you keep the warmth by proper insulating your house.
To keep your house cool, you should try to let in little sunlight, and any warmth that creeps in should be able to escape through open windows, say. If you want your house even cooler, you have to use air-conditioning. Then, you need to insulate your house to keep the house cool and put something in front of your windows (outside!), like "green curtains" (e.g. bitter melon).
