"Ze geeft de kleren aan haar zus."
Translation:She gives the clothes to her sister.
Well, "no logic" is not entirely true. Prepositions are just notoriously hard to translate one on one from English to Dutch, or any language for that matter.
Naar is used for a direction. "He is going to school" = hij gaat naar school.
Aan is used more freely. It can be, like in this sentence, for an indirect object: "He gives the pen to her" = Hij geeft de pen aan haar.
When referring to a position, there's usually a connection of some sorts involved. "He is hanging from the rock" = Hij hangt aan de rots; "She is bound to the pole" = Ze zit vast aan de paal. As you see, it's not necessarily the case that both aan and naar are translated with English "to". Rather than thinking of exact, literal translation, you should look to the different contexts aan or any other preposition is used in.