unter Hochdruck
under pressure
In a situation of great urgency, tension, or intense effort.
Das Team arbeitet unter Hochdruck an der Fertigstellung des Projekts.
The team is working under pressure to complete the project.

high pressure
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under pressure
In a situation of great urgency, tension, or intense effort.
Das Team arbeitet unter Hochdruck an der Fertigstellung des Projekts.
The team is working under pressure to complete the project.

The word is a simple compound of the adjective 'hoch' (high) and the noun 'Druck' (pressure). Its meaning is therefore literally 'high pressure' and is specialized in different contexts.
Der Kessel steht unter sehr hohem Druck.
The boiler is under very high pressure.
The context makes the meaning clear: 'unter Hochdruck' (under pressure) refers to work and stress. In a medical context, it refers to Bluthochdruck (high blood pressure). Technical devices use physical Hochdruck (high pressure), and in a weather forecast, Hochdruckgebiet (high-pressure system) is meant.
Die Entwickler stehen unter Hochdruck, die neue Software fertigzustellen.
The developers are under pressure to finish the new software.
The expression 'unter Hochdruck' (under pressure) is always used with the preposition 'unter' (under). It describes that someone is working on something very intensively and urgently or is under great stress.
Vor der Prüfung lernen die Studenten unter Hochdruck.
Before the exam, the students study under pressure.
In a medical context, 'Hochdruck' (high blood pressure) is often combined with the verbs 'haben' (to have), 'messen' (to measure), 'behandeln' (to treat), or 'senken' (to lower).
Viele Menschen haben leichten Hochdruck, ohne es zu wissen.
Many people have mild high blood pressure without knowing it.
In technology, 'Hochdruck-' (high-pressure) often forms the first part of compound words to describe a process or device. Examples are 'Hochdruckreiniger' (high-pressure cleaner), 'Hochdruckpumpe' (high-pressure pump), or 'Hochdruckgebiet' (high-pressure area, in physics).
Mit dem Hochdruckreiniger wird die Terrasse schnell wieder sauber.
With the high-pressure cleaner, the terrace quickly gets clean again.
In meteorology, 'Hochdruck' (high pressure) is a common abbreviation for 'Hochdruckgebiet' (high-pressure system). This term is typical of weather forecasts on the news or radio.
Der Meteorologe erklärte, dass der Hochdruck für das stabile Wetter verantwortlich ist.
The meteorologist explained that the high-pressure system is responsible for the stable weather.
pressure / printing
'der Druck' and 'der Hochdruck' overlap because 'Hochdruck' refers to a special form of pressure. 'Druck' is the general word, for example for physical pressure or for mental strain. 'Hochdruck' means literally or in technical contexts: especially high pressure, for example in technology, weather, or blood pressure. In the phrase 'unter Hochdruck', it also means very intensive work with a lot of urgency. The words can be confused because 'Hochdruck' seems like a stronger form of 'Druck'. Even so, 'Hochdruck' only fits in certain fixed or technical contexts.

Im Krankenhaus wird sein Hochdruck regelmäßig kontrolliert.
At the hospital, his high blood pressure is checked regularly.
Der Druck vor dem Abgabetermin macht das ganze Team nervös.
The pressure before the deadline is making the whole team nervous.