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.
How heat is lost
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.
Where cold and overheating is coming from
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