die Fackel
torch
A stick burning at one end that serves as a portable source of light, especially historically or outdoors.
Bei der nächtlichen Wanderung leuchteten uns die Fackeln den Weg.
During the nighttime hike, the torches lit our way.

torch
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torch
A stick burning at one end that serves as a portable source of light, especially historically or outdoors.
Bei der nächtlichen Wanderung leuchteten uns die Fackeln den Weg.
During the nighttime hike, the torches lit our way.

You can tell from context whether 'Fackel' (torch) is meant literally as a light source or figuratively as an idea. If it is about light, fire, or darkness, the literal meaning is intended. If it is about responsibility, ideas, or generations, the figurative meaning is intended.
Die Demonstranten zogen mit Fackeln durch die dunklen Straßen.
The demonstrators marched with torches through the dark streets.
In the literal sense, 'Fackel' (torch) is often combined with verbs such as 'anzünden' (to light), 'tragen' (to carry), or 'löschen' (to extinguish). The verb describes the direct action involving the light source.
Bevor sie die Höhle betraten, zündeten sie ihre Fackeln an.
Before they entered the cave, they lit their torches.
In the figurative meaning, 'Fackel' (torch) is almost always used in the fixed expressions 'die Fackel weitergeben' (to pass the torch) or 'die Fackel tragen' (to carry the torch). It symbolizes the transfer of a responsibility or an idea.
Der alte Firmenchef gab die Fackel an seinen Sohn weiter.
The old company director passed the torch to his son.
The meaning 'Zigarette' (cigarette) is purely colloquial and is used only in very informal situations among friends. In formal contexts, this usage is inappropriate.
Er ging auf den Balkon, um sich eine Fackel anzuzünden.
He went out onto the balcony to light up a smoke.
cigarette
'Zigarette' and 'Fackel' can mean the same thing in a special colloquial use. Normally, 'Zigarette' is the neutral and correct word for a small roll of tobacco used for smoking. 'Fackel' actually means something completely different, but it can rarely and informally be used as a word for a cigarette. In normal conversations, at school, at the doctor's, or in official texts, 'Zigarette' is much more natural. 'Fackel' as a cigarette is more likely to be understood as a casual or joking expression.

Auf der Party fragt Tom seinen Freund: „Hast du noch eine Fackel?“
At the party, Tom asks his friend, "Do you still have a smoke?"
Nach dem Essen geht mein Onkel nach draußen und raucht eine Zigarette.
After dinner, my uncle goes outside and smokes a cigarette.