The ESA is a supra-national organizatioon; some member organizations have their own space agencies for their own national imperatives. ESA has operated satellites and launched several missions to other planets and solar system bodies (such as Haley's Comet). ESA's Huygens probe was the first to return images of the liquid methane lakes on the surface of Saturn's moon Titan, in 2005. It does not operate launch vehicles, and does not have a human spaceflight program.
Though Arianespace is also another collaborative European commercial entity, it is not related to the European Space Agency.