To my understanding, both words translate to "fille." Are there any context independent translations?
As always the context is important. But you can't misunderstand the word fille in French, because there will always be an indication to help you know which meaning it has. If there is a possessive pronoun in front of it (or an equivalent) the meaning will be daughter.
C'est sa fille (She is his/her daughter)
Il s'agit de la fille d'un personnage important (She is the daughter of an important person)
If there is only a simple or no determinant in front of the word (or a demonstrative, etc...), the meaning will be girl.
C'est une fille de mon quartier (She is a girl from my neighbourhood)
Je suis allé à l'école avec cette fille (I went to school with this girl)
So even if both words girl and daughter have the same translation in French, you can easily know which meaning they have. The whole context is important, but sometimes if you just focus on the groupe nominal you can know if it means daughter or girl.
What does "besides from context" mean, if you are talking about the exact same word ("fille")? I cannot imagine what that would mean.
In terms of context, however (not your question, but hoping it might help):
Imagine that there is no word "daughter" in English. And imagine that in "my girl", "your girl", etc., "girl" always means daughter (which it sometimes does) and never means "girlfriend".
Now can you distinguish "girl" as daughter from other "girl"s? Yep. In French the two uses of "fille" are distinguished the same way.
"The Jones girl", "Sally's girl", "Bill's girl", "She had a girl", etc. all refer to the daughter meaning, in this scenario. And other uses of "girl", where you cannot understand a daughter relation, do not mean daughter. Simple as that.