The main purpose of an expansion tank is to compensate the variation of the volume of water due to the variation of the temperature in heating systems.
For example, the water heating up from 0°C to 100°C increases its volume of about 4,5%. This means that there should be a space inside the system that can keep the exceeding volume of water. This space is the expansion tank.
The main purpose of the pressure tank is to give water at a predefined pressure, regardless of boost pressure, in order to limit the pump insertions. This is due to the pressurised air that is between the membrane and the internal surface of the tank. When the pressure increases, the air cushion compresses letting the water filling in the tank. The water is kept inside the water tank under pressure.
FLAT EXPANSION TANKS FOR BOILERS