A diplomatic mission is a group of people from one state or an international inter-governmental organisation (such as the United Nations) present in another state to represent the sending state/organisation officially in the receiving state. In practice, a diplomatic mission usually denotes the resident mission, namely the office of a country's diplomatic representatives in the capital city of another country. As well as being a diplomatic mission to the country in which it is situated, it may also be a non-resident permanent mission to one or more other countries. There are thus resident and non-resident embassies.
An embassy is a permanent diplomatic mission, typically placed in the capital of the receiving country. An embassy is run by an ambassador, the foreign nation's highest-ranking representative in the nation receiving the mission.