Countries maintain two different kinds of mission abroad, and they do different jobs. The distinction explains where a traveller goes for help and where a government sends its diplomats.
One mission speaks to the state
An embassy is accredited to a host government and sits in the capital, because its work is conducted with ministries and officials.
It carries out negotiation, reports back on political and economic conditions, and represents its country's position to the officials who set the host state's policy.
There is normally one embassy per country, headed by an ambassador who is formally received by the host state and who serves as the single recognised channel between the two governments.
The other serves individuals
Consulates are placed in cities where a country's nationals live, travel or trade, which is why they appear well away from the capital.
Their work is administrative and practical: issuing and replacing passports, certifying documents, and assisting citizens who have been detained, hospitalised or bereaved a long way from home.
A country may run several consulates in a single host state, each covering a defined district rather than the whole territory, so which one a traveller deals with depends on where the problem occurred.
Visas sit on the consular side
Issuing visas is a consular function, which is why applications are handled by a consulate or by the consular section inside an embassy.
Large embassies contain such a section, and that is the source of the common assumption that embassies issue visas as a matter of course.
Decisions rest with individual consular officers applying the host country's own immigration law, and the specifics vary widely and change over time.
Diplomatic status is not identical
Diplomatic and consular privileges rest on separate international agreements, and the consular version is deliberately narrower, since consular officers deal with routine local business rather than affairs of state.
Both regimes protect the premises and the archives, which is the practical reason mission buildings cannot simply be entered or searched by local authorities on their own initiative.
Honorary consuls, often local residents appointed to represent a country part-time, hold a narrower status again and offer more limited services.
What happens when relations break down
When two states suspend diplomatic relations, the embassy usually closes while the practical need to serve citizens does not disappear.
A third country may then be asked to act as a protecting power, handling limited consular matters on behalf of the departed mission.
That arrangement is the reason citizens can sometimes still obtain documents in a country whose government their own no longer formally recognises.