1 o'clock in the morning OR 1 o'clock at night?

Actually, its a bit confusing because even in English, both (morning and night) could be correct depending on the context.

Firstly, its fine to say that 11PM to 4AM is night time, because the sky is obviously dark outside and visibility is almost non-existent.

But its also correct to say "2AM in the morning" because all the international timezones consider 12:00 AM midnight to be the time when the date changes. And since by definition, morning is the time when a day starts or begins, its perfectly fine to say "I'm writing this answer at 2AM in the morning" because the day (17th June) has just started two hours ago.

Morning means after I wake up. Night means after I go to bed. 1 o'clock in the morning means you've woken me up so knock off that damn racket. 1 o'clock at night means I've have fun staying up late so stop complaining about the racket I'm making. So yes they both mean 1 am.

The way we talk about time has a lot to do with how we feel about it.

1 pm is of course expressed as 1 o'clock in the afternoon.