The prepositions below and under have similar meanings. Both can mean ‘lower than’.

Cases where below is preferred

Below can mean ‘at or to a lower level’.

The people in the apartment below seldom go out.
Put your signature below.
I feel sick, I must go below. (= I must go downstairs to my cabin.)

Below: not directly under

We use below when one thing is not directly under another.

The sun sank below the horizon.
The climbers stopped 200m below the top of the mountain.

Below is used in measurements where we think of a vertical scale.

The temperature is ten degrees below zero.
The Dead Sea is below sea level.
She is below average in intelligence.

Cases where under is preferred

We prefer under when something is covered by what is over it. Under is also used when things are touching.

There is something under the bed.
He wore a shirt under his sweater.

Under can mean ‘less than’ or ‘younger than’. Below is not used with this meaning.

There were under twenty people at the meeting. (= There were less than twenty people.)
You can’t vote if you are under 18. (NOT You can’t vote if you are below 18.)