Your boiler runs a closed system. The radiators, pipes, and boiler are separated from the world by the fill valve and pressure relief valve. Normally those are both closed. The system must have an expansion tank and that tank only serves the closed system.

Your water heater may or may not need an expansion tank. If you have a pressure reducer it does, otherwise it does not need one because the pressure is defined by the supply and an expansion tank would do nothing.

A leaky hot water pressure relief valve may be a sign that you do need one or it may just be dirty or faulty.

Your boiler runs a closed system. The radiators, pipes, and boiler are separated from the world by the fill valve and pressure relief valve. Normally those are both closed. The system must have an expansion tank and that tank only serves the closed system.

If you have a pressure reducer or check valve on your main water supply your water heater also needs an expansion tank. If you have no such valve an expansion tank would do nothing as the pressure is defined by the supply.

A leaky hot water pressure relief valve may be a sign that you do need one or it may just be dirty or faulty. Note that a pressure relief valve that is leaking because of the lack of an expansion tank may also as a result, develop an inherent leak caused by continuous deposit of calcium in the mechanism. In other words, it may not have been faulty but it may keep leaking after you install an expansion tank and may need to be replaced.