Is the sentence "I didn't marry you because you were rich." same as " I married you not because you were rich but for another reason."
They both express the same idea -- that a reason other than wealth is why the speaker married the subject. The first sentence is more likely to be ambiguous, as Peter Shor noted:
- is the speaker married to the subject, for a reason other than wealth?
- is the speaker not married to the subject, because they're rich?
In either case, a native speaker would probably expect to hear a parallel structure for each sentence. For example:
I didn't marry you because you were rich. [I married you because you were my soulmate.]
I married you not because you were rich, [but because you were my soulmate].
Without the parallel construction, the first sentence sounds a little more natural.