Passer vs. s'écouler

The French words 'passer' and 's'écouler' both convey the concept of time moving forward or events taking place over time. However, there are nuances in their usage and contexts that distinguish them from each other.

Passer

'Passer' is a versatile verb used to indicate the passage of time, but it can also refer to physically passing by a place or an object. It is generally less formal and can be used in various contexts.
Le temps passe vite quand on s'amuse.
(Time flies when you're having fun.)
Nous sommes passés devant la cathédrale hier.
(We passed by the cathedral yesterday.)
Laissez passer quelques jours avant de prendre une décision.
(Let a few days go by before making a decision.)

S'écouler

'S'écouler' is more specific and formal, primarily used to describe the flow or elapse of time without a focus on movement through space. It often carries an implication of time moving inexorably or naturally, like water flowing.
Plusieurs années se sont écoulées depuis notre dernière rencontre.
(Several years have elapsed since our last meeting.)
Du temps s'est écoulé avant qu'il ne réponde à la question.
(Some time passed before he answered the question.)
L'eau s'écoule lentement dans le ruisseau.
(The water flows slowly in the stream.)

Summary

In summary, 'passer' is a more general term that could mean to pass by physically or for time to go by, and it fits well in informal speech and writing. On the other hand, 's'écouler', usually referring only to the passage of time, leans towards a more formal style and often connotes a natural or inevitable passage similar to that of flowing water. Understanding the nuances of these verbs can help one choose the appropriate word based on context and formality.