rauf
up
Colloquial short form of 'herauf' or 'hinauf', expressing movement upward.
Wir müssen den ganzen Berg zu Fuß rauf.
We have to go up the whole mountain on foot.

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up
Colloquial short form of 'herauf' or 'hinauf', expressing movement upward.
Wir müssen den ganzen Berg zu Fuß rauf.
We have to go up the whole mountain on foot.

'Rauf' (up) is the colloquial and very common short form of 'herauf' or 'hinauf' (upward/up here/up there). In formal or written texts, the full words are usually used.
Kommst du kurz rauf? Ich brauche deine Hilfe.
Can you come up for a moment? I need your help.
'Rauf' (up) is often combined as a separable prefix with verbs of movement (e.g. 'raufgehen' (to go up), 'raufklettern' (to climb up), 'rauffahren' (to drive/ride up)). In a main clause, 'rauf' goes at the end.
Wir gehen den Berg jetzt rauf.
We're going up the mountain now.
The expression 'rauf und runter' (up and down) means 'repeatedly' or 'very thoroughly'. For example, you can 'rauf und runter singen' (sing something over and over) a melody or 'rauf und runter beten' (recite something over and over) a poem.
Ich kenne den Text mittlerweile rauf und runter.
By now I know the text up and down.
high
'hoch' and 'rauf' both relate to being up or above. 'hoch' is an adjective and describes a height or a high position. 'rauf' is an adverb and describes movement upward. It is also colloquial and sounds more natural in conversation than in formal texts. They can be confused because in everyday speech you often also hear 'hoch' with movements, for example 'die Treppe hoch' (up the stairs). For direction, however, the more precise standard-language word is 'hinauf', or colloquially 'rauf'.

Komm bitte kurz rauf, ich brauche deine Hilfe im dritten Stock.
Please come up for a moment; I need your help on the third floor.
Für das Konzert haben wir eine hohe Bühne aufgebaut.
We built a high stage for the concert.