die Säge
saw
A tool with a toothed blade that is used to cut through materials such as wood, metal, or plastic with cutting motions.
Mit der Säge schnitt er die Bretter für das Regal zu.
He cut the boards for the shelf to size with the saw.

saw
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saw
A tool with a toothed blade that is used to cut through materials such as wood, metal, or plastic with cutting motions.
Mit der Säge schnitt er die Bretter für das Regal zu.
He cut the boards for the shelf to size with the saw.

'Die Säge' (the saw) is the tool that belongs to the activity 'sägen' (to saw). If you know the verb, you can easily infer the meaning of the noun.
Er sägt das Holz mit einer neuen Säge.
He is sawing the wood with a new saw.
You can easily recognize the meaning from the context. If people are talking about crafts, wood, or construction work, the tool is meant. If the word is used as an insult or to describe a person, it refers to the nagging person.
Ich brauche eine Säge, um diesen Ast abzuschneiden.
I need a saw to cut off this branch.
Using 'Säge' (nag/old hag) for a person is very colloquial and derogatory. Use this expression only if you are aware of its negative effect.
Er nannte seine Chefin im Streit eine „alte Säge“.
During the argument, he called his boss an 'alte Säge' (old hag).
chainsaw
'die Säge' and 'die Kettensäge' are both tools used to cut through things, especially wood. 'die Säge' is the more general term. It can be a simple hand saw or another kind of saw. 'die Kettensäge' is a specific motor-powered saw with a moving chain. It is more likely to be used for thick branches, tree trunks, or work in the forest. Learners may confuse the words because every chainsaw is a saw. But not every saw is a chainsaw.

Für das kleine Brett reicht eine einfache Säge aus.
A simple saw is enough for the small board.
Nach dem Sturm zerschnitt der Förster den umgefallenen Baum mit der Kettensäge.
After the storm, the forester cut up the fallen tree with the chainsaw.