English term corresponding to German “Ausgangssperre”
In English,
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Curfew refers to a time imposed by the authorities where you can’t be on the streets after a certain time at night. You can travel all you want during the day but you can’t be outside at night after curfew, a given time starting in the evening. Presumably curfew lasts until daybreak. If you’re over at a friends place, you’ll have to stay there, you can't go out until morning. I suppose a curfew could be for anytime of the day, but the first thought is that it is for nighttime. The rule is imposed for as long as the authorities say, while you're still under occupation or you're still a teenager.
The invaders imposed a curfew to help prevent local insurrection.
When I was 16, my parents gave me a curfew of 11pm so I wouldn’t stay out too late and get into trouble.
If you break curfew, you may be arrested. Curfew has the negative connotation of oppression and being punitive.
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Quarantine refers to the condition of being kept in a single place while you’re sick or infectious. Quarantine may be at a hospital, medical facility, or at one’s own home. You can’t leave, all day every day, until the doctor says so, which could be for days or weeks.
People with tuberculosis need to be kept in quarantine until antibiotics have cured them.
Leaving quarantine is not nominally a civil offense, but it is a medical hazard. Quarantine has the negative connotation of being sick and communicable. It's not a punitive measure (you didn't do any thing to deserve it, it's not a punishment).
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Shelter in place is a recent phrasing (to me at least) used by authorities as a recommendation (maybe it is just a euphemism for an order?) to stay at home.
The black bear was seen walking into the neighborhood coffee shop. Until the animal control people have captured the bear, please shelter in place. It should take no longer than two hours.
'Shelter in place' has only the slightest negative connotation in that something bad must be going on to need it, but there's no panic involved because you're just waiting.
Quarantine and curfew are nearby but would never be confused in English. Quarantine is for sickness and is continuous, curfew is for police control and is (usually) just for nighttime.
What I’ve found as translation for Ausgangssperre on Leo was curfew, but it seems like you can use the German word for other things like quarantine, though the translation of quarantine they give to German is the transparent Quarantäne.
I'd suggest lockdown it has certain prison-ey connotations, but definitely has the negative slightly ambiguous 'you must obey' style vibe.