der Fernseher
television / TV
An electronic device with a screen that is used to receive and play television programs; a TV set.
Wir haben uns einen neuen, größeren Fernseher gekauft.
We bought ourselves a new, bigger television.

television
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television / TV
An electronic device with a screen that is used to receive and play television programs; a TV set.
Wir haben uns einen neuen, größeren Fernseher gekauft.
We bought ourselves a new, bigger television.

'Fernseher' is composed of 'fern' (far away) and 'sehen' (to see). The ending '-er' here refers to the device that makes the action possible. So a 'Fernseher' is literally a 'far-seer'.
Früher waren Fernseher große, schwere Kisten.
In the past, televisions were big, heavy boxes.
The word 'der Fernseher' always refers to the physical device. The activity of watching TV is expressed with the verb 'fernsehen' (to watch TV).
Der Fernseher ist kaputt, deshalb können wir heute Abend nicht fernsehen.
The television is broken, so we can't watch TV tonight.
Common verbs related to the device are 'den Fernseher einschalten' (to turn on the television), 'ausschalten' (to turn it off), or 'umschalten' (to change channels). 'Vor dem Fernseher sitzen' (to sit in front of the television) is also a very typical phrase.
Kannst du bitte den Fernseher etwas leiser machen?
Can you please turn the television down a bit?
TV
'der TV' and 'der Fernseher' can both mean the device you watch television on. 'der Fernseher' is the normal, clear everyday word. 'der TV' is a short form and often sounds a bit more modern or advertising-like, for example when buying a device. The words can be confused because they are almost the same in this meaning. The important point is simply: 'TV' can also mean the medium or the program, while 'Fernseher' always means the device.

Der Fernseher bleibt heute Abend aus, weil wir lesen wollen.
The TV will stay off this evening because we want to read.
Er hat heute einen neuen TV für das Wohnzimmer gekauft.
He bought a new TV for the living room today.