Consulates
From Wikipedia,

Consulates are more numerous than diplomatic missions (e.g. embassies), since the latter are posted only in a foreign nation's capital (exceptionally even outside the country, in case of a multiple mandate, e.g. a minor power may well accredit a single Ambassador with several neighbouring states of modest relative importance that are not considered important allies), while consular ones are also posted in various cities throughout the country, especially centres of economic activity, or wherever there is a significant population of its citizens (expatriates) in residence.

In large foreign cities a sovereign state may be represented by a senior consul known as a consul-general, who typically has several consuls and vice consuls working under him/her. The office of a consul-general is known as a consulate-general. Consulates-general need not be in the capital city, but instead in the most appropriate cities. In the United States, for example, many countries base their consulate-general in New York City.

A consul is a representative of a sovereign state, posted to a foreign territory, in charge of matters related to individual people and businesses, in other words issues outside inter-governmental diplomacy. The office of a consul is known as a consulate.

Embassies / Diplomatic Mission

embassy (plural embassies)

1. organization that permanently represents a sovereign state in a second sovereign state or with respect to an international organization such as the United Nations
        The American embassy to France is located in Paris.
2. the building in which such an organization is located

From Wikipedia,

A diplomatic mission is a group of people from one state or an international inter-governmental organization (such as the United Nations) present in another state to represent the sending state/organization in the receiving state. In practice, a diplomatic mission usually denotes the permanent mission, namely the office of a country's diplomatic representatives in the capital city of another country.

A permanent diplomatic mission is usually known as an embassy, and the head of the mission is known as an ambassador.

• Embassies and Consulates Worldwidee - Information and links in English, French, Spanish and German.
• Embassy World - Searchable global directory providing contact information and links to Web pages (if available) for embassies and consulates around the world, US embassies abroad, foreign embassies in the US, and permanent missions to the UN.
• Governments on the WWW: Representations in Foreign Countries - A single-page list of to the websites of many embassies and consulates.