die Stille
silence
A state in which there are no sounds; complete noiselessness or quiet.
Nachdem der Motor ausging, herrschte eine unheimliche Stille.
After the engine stopped, an eerie silence fell.

silence / stillness
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silence
A state in which there are no sounds; complete noiselessness or quiet.
Nachdem der Motor ausging, herrschte eine unheimliche Stille.
After the engine stopped, an eerie silence fell.

The noun 'die Stille' (silence/stillness) is derived from the adjective 'still' (quiet/still). When a place or situation is 'still', then there is 'Stille' there.
Sei bitte still, ich brauche etwas Stille zum Arbeiten.
Please be quiet; I need some silence to work.
'Stille' (silence/stillness) is often combined with certain verbs that describe a state. Typical phrases are 'Stille herrscht' (silence reigns/there is silence), 'Stille tritt ein' (silence falls), or 'die Stille genießen' (to enjoy the silence/stillness).
Als der Redner eine Pause machte, trat plötzlich Stille im Saal ein.
When the speaker paused, silence suddenly fell in the hall.
The expression 'in aller Stille' means that something happens secretly, unnoticed, or without much publicity.
Das Paar hat in aller Stille geheiratet, ohne Gäste einzuladen.
The couple got married quietly, without inviting any guests.
quiet / calm
'die Ruhe' and 'die Stille' are close in meaning when it comes to little or no noise. 'die Stille' especially emphasizes that truly nothing, or almost nothing, can be heard. 'die Ruhe' is a bit broader: it can also mean that you are not disturbed or that you are inwardly relaxed. That is why a place can be ruhig even if you hear quiet sounds. Learners may confuse the words because both often fit quiet places. If you mean noiselessness, 'Stille' is more precise; if you mean relaxation or being undisturbed, 'Ruhe' fits better.

Nach dem Sturm lag eine tiefe Stille über dem Dorf.
After the storm, a deep silence lay over the village.
Im Urlaub hat Tim endlich die Ruhe, ein Buch zu lesen.
On vacation, Tim finally has the peace and quiet to read a book.