das Theater
theater
A building in which plays, operas, or other performing arts are performed in front of an audience.
Die Vorstellung im Deutschen Theater war ausverkauft.
The performance at the Deutsches Theater was sold out.

theater
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theater
A building in which plays, operas, or other performing arts are performed in front of an audience.
Die Vorstellung im Deutschen Theater war ausverkauft.
The performance at the Deutsches Theater was sold out.

'Das Theater' (theater) refers to a place for live performances such as plays or opera. A place where films are shown is called 'das Kino' (cinema/movie theater) in German, not 'Theater'.
Wir gehen heute Abend ins Theater, um uns ein Musical anzusehen.
We're going to the theater tonight to see a musical.
You can recognize the different meanings from the sentence structure. 'Ins Theater gehen' (to go to the theater) refers to the building. 'Sich für Theater interessieren' (to be interested in theater) refers to the art form. The exclamation 'Mach kein Theater!' (Don't make a fuss!) refers to exaggerated behavior.
Die Karten für das große Theater sind teuer.
Tickets for the big theater are expensive.
Pay attention to the case with the preposition 'in': Movement toward the place is expressed with the accusative ('ins Theater' — to the theater), while being at the place is expressed with the dative ('im Theater' — in/at the theater).
Morgen Abend gehen wir ins Theater.
Tomorrow evening we're going to the theater.
The figurative meaning is very often used in the fixed expression 'ein Theater machen' (to make a fuss). This means that someone is dramatizing a situation or making an unnecessary big deal out of something.
Er macht immer ein riesiges Theater, wenn er eine Spritze bekommen soll.
He always makes a huge fuss when he has to get an injection.
The meaning 'exaggerated behavior' is especially common in colloquial language. In formal situations, this expression is generally avoided.
Hör auf mit dem Theater und iss dein Gemüse!
Stop with the drama and eat your vegetables!
show
'die Show' and 'das Theater' can both have to do with performances and entertainment. A 'Show' is often an entertaining event or program, for example with music, guests, or special effects. 'Theater' usually means the building, the art form, or a stage play. Both words also have a figurative meaning: 'Show' can mean fake or attention-grabbing behavior, while 'Theater' more often means exaggerated arguing or unnecessary fuss. They can be confused because both can take place on a stage. For the building or classical drama, 'Theater' fits better; for modern entertainment or television, 'Show' is more likely.

Nach dem Kurs gehen wir ins Theater und sehen ein Stück.
After the course, we're going to the theater to see a play.
Die Show im Fernsehen hatte viele Gäste und laute Musik.
The show on TV had many guests and loud music.