
die Stunde
hour
A unit of time that lasts 60 minutes.
Ich warte schon seit über einer Stunde auf den Bus.
I've been waiting for the bus for over an hour.
hour
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hour
A unit of time that lasts 60 minutes.
Ich warte schon seit über einer Stunde auf den Bus.
I've been waiting for the bus for over an hour.

class / lesson
A teaching unit at school or in a course, usually 45 or 90 minutes long.
In der nächsten Stunde schreiben wir einen Test in Geschichte.
In the next class, we are writing a history test.

hour / moment
A special, often fateful or important moment in life or in history.
Das war die dunkelste Stunde seines Lebens.
That was the darkest hour of his life.

at present
A formal expression for 'now' or 'at this moment'.
Zur Stunde können wir noch keine genauen Angaben machen.
At present, we cannot yet provide any exact information.
'Stunde' (hour) is used with various prepositions for time expressions. 'In einer Stunde' describes a point in the future, 'vor einer Stunde' a point in the past, and 'seit einer Stunde' a duration that continues up to now.
Der Zug fährt in einer Stunde ab.
The train leaves in an hour.
In the context of school, university, or courses, 'Stunde' almost always means 'Unterrichtseinheit' (class/lesson) and not 60 minutes. Signal words are subjects like 'Mathe' (math), 'Deutsch' (German), or words like 'Lehrer' (teacher) and 'Unterricht' (instruction/class).
In der ersten Stunde haben wir heute Englisch.
In the first class today, we have English.
In this meaning, 'Stunde' is used in an elevated, often literary or emotional style to describe a decisive moment. Typical expressions are 'die Stunde der Wahrheit' (the moment of truth) or 'in der Stunde der Not' (in the hour of need).
In seiner schwersten Stunde waren seine Freunde für ihn da.
In his most difficult hour, his friends were there for him.
The expression 'zur Stunde' (at present) is a very formal way to say 'now' or 'currently'. You find it mainly in news reports, official announcements, or speeches.
Der Präsident ist zur Stunde nicht erreichbar.
The president is not reachable at present.
moment
Stunde and Moment can both refer to an important point in time. Stunde sounds ceremonial and presents the event as a significant phase in history. Moment focuses more on a single, brief, or precisely defined instant.

Die Öffnung der Grenze war eine historische Stunde für das Land.
The opening of the border was a historic moment for the country.
Der Moment der Grenzöffnung wurde im Fernsehen übertragen.
The moment the border opened was broadcast on television.