"She is eating breakfast because she is hungry."
Translation:Hun spiser frokost for hun er sulten.
No, not quite. If you use fordi, you can invert the order of the clauses:
“Fordi hun er sulten, spiser hun frokost.”
You cannot do this with for.
Another difference is with word order. Let’s negate this sentence so that is says that “she doesn’t eat breakfast because she’s not hungry”. Then the alternatives are:
“Hun spiser ikke frokost, for hun er ikke sulten.”
“Hun spiser ikke frokost fordi hun ikke er sulten”.
Note that er and ikke swap places. (It’s similar if you use another adverb, such as kanskje.)
Finally there is a small difference in that in sentences such as these there should be a comma before for but not before fordi. Thus:
“Hun spiser frokost fordi hun er sulten.”
“Hun spiser frokost, for hun er sulten.”
(The comma is apparently left out in the official translation here. This is strictly speaking an error.)
The grammatical explanation for these differences is that for is a coordinating conjunction (konjunksjon), while fordi is a subordinating conjunction (subjunksjon). Thus for behaves in the same way as the other coordinating conjunctions (namely og, men and eller), while fordi behaves in the same way as other subordinating conjunctions (such as når, mens and at).