die Ecke
corner
The point or area where two lines, surfaces, or streets meet.
Wir treffen uns an der Ecke Hauptstraße und Schillerstraße.
We'll meet at the corner of Hauptstraße and Schillerstraße.

corner
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corner
The point or area where two lines, surfaces, or streets meet.
Wir treffen uns an der Ecke Hauptstraße und Schillerstraße.
We'll meet at the corner of Hauptstraße and Schillerstraße.

The preposition reveals the location. 'An der Ecke' (at the corner) describes a position on the street (dative). 'In der Ecke' (in the corner) describes a position in a room (dative).
Der Briefkasten befindet sich an der nächsten Ecke.
The mailbox is located at the next corner.
The expression 'um die Ecke' (around the corner) often does not literally mean that you go around a corner, but that something is very close. This is often emphasized with 'gleich' (right) or 'direkt' (directly).
Keine Sorge, der Supermarkt ist gleich um die Ecke.
Don't worry, the supermarket is right around the corner.
The expression 'jemanden um die Ecke bringen' (to bump someone off) is a colloquial and figurative way of saying 'jemanden töten' (to kill someone). The structure is fixed: the subject bringt the accusative object um die Ecke.
Im Film versucht der Bösewicht, den einzigen Zeugen um die Ecke zu bringen.
In the film, the villain tries to bump off the only witness.
When talking about a street corner, typical verbs are 'stehen' (to stand), 'warten' (to wait), or 'sich treffen' (to meet).
Ich warte an der Ecke auf dich.
I'll wait for you at the corner.
area / field
'der Bereich' and 'die Ecke' can both mean part of a room or an area. 'Der Bereich' sounds more general and often somewhat more clearly defined, for example an area in a building or on a site. 'Die Ecke' is smaller and usually means the place at an edge or where two sides meet. You can confuse the words when talking about part of a room. For a zone with a specific function, 'Bereich' fits better. For a small place at the edge or in an angle, 'Ecke' sounds more natural.

Die alten Kisten stehen hinten in der Ecke.
The old boxes are in the back corner.
Der Bereich vor dem Eingang bleibt wegen der Bauarbeiten gesperrt.
The area in front of the entrance remains closed because of the construction work.