screen
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screen
The flat, illuminated surface of an electronic device such as a computer, television, or smartphone, on which images and text are displayed.
Ich arbeite den ganzen Tag am Bildschirm und meine Augen sind müde.
I work at the screen all day and my eyes are tired.
The word is made up of 'Bild' (image/picture) and 'Schirm' (screen/shield). So it literally describes a screen that displays images.
Der neue Computer hat einen sehr großen Bildschirm.
The new computer has a very large screen.
To describe an activity, you use 'am Bildschirm arbeiten' (to work at the screen). To describe the position, you say 'vor dem Bildschirm sitzen' (to sit in front of the screen). The direction of one's gaze is expressed with 'auf den Bildschirm schauen' (to look at the screen).
Sie sitzt den ganzen Tag vor dem Bildschirm.
She sits in front of the screen all day.
Common verbs in connection with the screen are 'einschalten' (to turn on), 'ausschalten' (to turn off), and 'sperren' (to lock). In online meetings, 'den Bildschirm teilen' (to share the screen) is also very common.
Kannst du bitte deinen Bildschirm teilen, damit wir das Dokument sehen?
Could you please share your screen so we can see the document?
The idiom 'jemanden/etwas auf dem Bildschirm haben' (to have someone/something on one's radar) means that you are observing or taking a person or thing into account. It is not about a real screen here, but about attention.
Die Konkurrenz hat ein neues Produkt angekündigt, das sollten wir auf dem Bildschirm haben.
The competition has announced a new product; we should have that on our radar.
window
'das Fenster' and 'der Bildschirm' can both have to do with computers. The screen is the whole surface of a device where you see text and images. A window is only one area on this screen, for example a program window. Learners may confuse the words because something is displayed in both. As a practical rule: you look at the screen, but you open, close, or move a window.
Auf dem Bildschirm erscheint eine Nachricht von der Ärztin.
A message from the doctor appears on the screen.
Tom schließt das Fenster, weil das Programm nicht mehr reagiert.
Tom closes the window because the program is no longer responding.