© Tobias Woelke 2021
The verb “hoffen” is used in contexts of “trust, hope, desire”.
Some examples:
Wir hoffen, dass Klaus die Prüfung besteht.
We hope that Klaus will pass the exam.
Sie hoffen auf das Beste
They hope for the best
On the other hand the verb “erwarten” is rather used in a context of “expecting something from someone”.
Some examples:
Wir erwarten, dass Klaus die Prüfung besteht
We expecting, that Klaus will pass the exam
Die Touristen erwarten immer das Beste
Tourists always expect the best
Markus erwartet von Hans das Geld zurück
Markus expects Hans to give him his money back
In this link you can read more about some of the words that cause some confusion for people learning German:
https://successgerman.com/what-is-the-difference-between-anwenden-nutzen-and-benutzen/