These are both tools that are used for measurement but the hygrometer is in charge of measuring the amount of water vapor that can be found in the air. This means that it will measure the water vapor found in the air. The hydrometer, based on its name, will measure the density of the liquid that can be found in a specific area.
The hydrometer is normally made out of glass and it comes with a tube that comes with mercury or lead shot. This will make sure that this will stay upright and that it will float properly. The hygrometer is being used because it is important to measure humidity in our surroundings.