Срок: term, duration, deadline
According to the great etymologist Max Fasmer, when ancient Russians wanted to cut a deal, they said something like съреку, which meant "I agree." Сърокъ was what they agreed to — соглашение (agreement).
Unfortunately, Fasmer is silent on whether these ancients shook hands, bumped foreheads or just celebrated the deal with some home brew.
In any case, over time срок has narrowed in meaning. It is no longer the agreement, but just part of it — its duration or the moment the agreement is up. And the notion of agreement itself has become abstract or disappeared altogether.
Today, срок is any kind of time period, like срок аренды (term of rental agreement), срок действия договора (period of contract validity), срок хранения продукта (product shelf life) or срок службы оборудования (equipment service life).
It's the word used to describe a term in office: Медведев решил не идти на второй срок (Medvedev decided not to run for a second term). It's also the word used to describe a jail term, which is the source of endless puns, particularly in newspaper headlines: Лондонцы дали мэру Джонсону второй срок (Londoners sentenced Mayor Johnson to a second term).
But срок can also refer to the moment a contract is up or a piece of work is due. Here there is a lot of linguistic variety. For example, you can say к сроку (by the deadline) or в срок (in the time period), both of which mean "on time." Строители сдали объект в срок (The builders finished the structure on time).
When a client asks me to do a translation, I always ask: Когда крайний срок? (When is the deadline?). The answer is often, of course: Вчера (Yesterday).
Deadlines are often described in the plural in Russian, even if you are talking about just one: Я не успеваю по срокам! (I can't meet the deadline!) Мы выполнили работу в напряжённые сроки (We finished the work on a really tight schedule). В кратчайшие сроки is what Americans call ASAP. Мы гарантируем доставку письма в Америку в кратчайшие сроки (We guarantee postal delivery to America in the shortest time possible).
When a job is really urgent, you can call it аврал or авральная работа. The origins of the word аврал might surprise native English speakers. Most Russian dictionaries assert that it is a corruption of the English "over all" and state that this phrase is shouted on a ship to mean "all hands on deck." Oddly, in all these dictionaries "over" is defined as наверх (up, above), yet no English nautical dictionary I can find supports this.
More authoritatively, in movies when a ship hits rough water or is under attack, the captain never shouts "Over all!" Even Fasmer is rather reticent on this topic, but he does cite the Dutch "overal" (defined as "everywhere") as the source. Given that Peter the Great founded the Russian Navy after his Dutch adventure, this sounds more likely to me.
In any case, when your boss or client shouts "Аврал!" it means, "Get cracking!"
When I ask a translation client — in a squeaky, pathetic voice — Это срочно? (Is it urgent?), I'm always happy to hear: Нет, не срочно (No, it's not urgent). Не горит (There's no hurry; literally "it's not burning"). Терпит (It can wait). Без спешки (No rush). Когда получится (Whenever you can).
I'll bump foreheads over that kind of deal any day.