"Von" is closer to "from", while "aus" is closer to "out (of)", but being prepositions, they can have many equivalents and uses depending on the context, and it is a matter of experience to know what to use when - sorry...

Das Buch fällt von dem Tisch: The book falls from the table. Das Buch wurde geschrieben von ihm: The book was written by him. Ich nehme das Buch aus dem Schrank: I take the book out of the cupboard.