The above picture is self explanatory about the difference between two major equipment of packages.
The cooling tower cools down the water droplet temperature through air. However the chiller cool down the coolant in the system.
The chillar comprises of compressor and evaporator. The chiller could be air cooled or water cooled. The air cooled chiller occupy more space and is not suitable where space is a constraint.The air or water used here is getting cooled at different places .
That water can be cooled at cooling tower.
Cooling towers are designed in two major types: mechanical draft and natural draft.
Mechanical draft cooling towers rely on fans to pull cool air into the system to remove the heat from water. Natural draft towers, commonly seen with a nuclear power plant, use the exhaust air funneled into a tall chimney. As the air rises, it provides cooling properties.
Chillers are designed as radiators, which are either water-cooled or air-cooled. Air-cooled chillers need less maintenance than water-cooled chillers, while the latter consumes less power than the former.