An embassy is a building where diplomats from one world can live and/or work on the territory of another. Many worlds have embassies on Earth, which is the capital of the United Federation of Planets. A consulate is a sub-division of an embassy.
During the 22nd century, the Vulcans had consulates in Berlin, Canberra and San Francisco. (ENT: "Fusion", "Terra Prime")
The United Earth Embassy on Vulcan was bombed in 2154. (ENT: "The Forge")
Early in his Obsidian Order career, Elim Garak was posted to the Cardassian embassy on Romulus. According to Garak, however, he was merely a gardener there. (DS9: "Broken Link", "Inter Arma Enim Silent Leges")
- According to a line cut from DS9: "The Wire", Benjamin Sisko was also assigned to Romulus, when he was posted at the Federation embassy there during the late 2350s. However, that would have been inconsistant with the fact that the Romulans were in isolation until 2364.
Lisa Cusak once worked at the Federation embassy on Andor. While there she started a long relationship with an Andorian who worked at the Andorian Agricultural Ministry. (DS9: "The Sound of Her Voice")
Verad was the communications clerk of the Federation consulate on Khefka IV. (DS9: "Invasive Procedures")
The Klingons and the Federation maintained consulates, the Vulcans an embassy on Deep Space 9's Promenade by 2370. (Star Trek: Deep Space Nine set decoration)
- According to the decoration there also was a Bajoran consulate on the promenade, but since DS9 was Bajoran territory this would make no sense.
One of Odo's friends in Starfleet Intelligence was formerly assigned to the Federation embassy on Qo'noS. This friend of Odo's still had a contact with a former agent of Klingon Intelligence by 2371. (DS9: "Visionary")
Gul Dukat suggested that if he was to get his position back as Military Advisor to the Detapa Council, he would post Gul Marratt to the Cardassian embassy on Breen in 2372. (DS9: "Return to Grace")
In 2374, the Orion Syndicate planned, attempted and failed an attempt to break into the Klingon embassy on Farius Prime to assassinate their Ambassador. (DS9: "Honor Among Thieves")