Hi, let me try to answer this one.
Consulate is the office for a consul and embassy is the office for an ambassador.
An ambassador is an important official who lives in a foreign country to represent his or her own country there, and who is officially accepted in this position by that country. A consul is an official chosen by a government to live in foreign city, in order to take care of people from the official's own country who travel or live there, and to protect the trade interests of that government.
As far as I know, ambassador will only stay in the capital of the foreign country. We can have conculs in many key cities. For example, we have American ambassador in Beijing but consuls in Shanghai, Hong Kong etc.