die Geschichte
story
A narrated or written sequence of events that may be true or invented; a narrative.
Kannst du mir eine Geschichte zum Einschlafen vorlesen?
Can you read me a bedtime story?

story / history
Loading your saved state.
story
A narrated or written sequence of events that may be true or invented; a narrative.
Kannst du mir eine Geschichte zum Einschlafen vorlesen?
Can you read me a bedtime story?

'Geschichte' (story/history) is closely related to the verb 'geschehen' (to happen, to occur). So a 'Geschichte' is literally something that has 'geschehen' (happened).
Was ist denn hier geschehen?
What happened here?
The context makes it clear whether 'story' or 'history' is meant. If it is about personal narratives, books, or films, it means 'story'. If it is about the past of countries or the academic field, it means 'history'.
Er hat mir die ganze Geschichte von seinem Urlaub erzählt.
He told me the whole story about his vacation.
When 'Geschichte' (story) means a narrative, it is often combined with verbs such as 'erzählen' (to tell), 'schreiben' (to write), 'erfinden' (to invent), or 'vorlesen' (to read aloud).
Mein Opa kann sehr gut Geschichten erzählen.
My grandpa is very good at telling stories.
In everyday language, 'die Geschichte' (the matter/affair) can also refer to a complicated or unpleasant matter. This use is informal.
Die Geschichte mit dem kaputten Auto hat viel Geld gekostet.
The affair with the broken car cost a lot of money.
thing / matter
'die Geschichte' and 'die Sache' can both mean a matter or a problem. 'die Sache' is more neutral and very general: you can talk about a topic, a plan, or a problem. In this meaning, 'die Geschichte' sounds more colloquial and often a bit more personal or complicated. Learners may confuse the words because in conversations you can sometimes say both. A simple guideline is: for a neutral matter, 'Sache' usually fits better; 'Geschichte' fits more when something sounds like an incident or a complicated situation.

Die Geschichte mit dem verlorenen Schlüssel hat den ganzen Abend gedauert.
The whole affair with the lost key took up the entire evening.
Nach dem Gespräch war die Sache für alle klar.
After the conversation, the matter was clear to everyone.