particle の - What is the difference between 「女性一人」 and 「一人の女 性」?

So far, I've learnt that a quantity (number + counter) can be attached to a noun to quantify it by using の:

一人の女性。One woman.

However, I came across a sentence in my textbook where the noun an the number+counter are grouped in the opposite order and withouta any particle:

女性一人。One woman.

I wonder if there is any difference in terms of meaning, usage or style for each possibility.

You can check the original answer in the Japanese Stack Exchange from which my question arised here. It might provide the context necessary to address this question.

よろしくお願いします！

EDIT: the question was identified as a duplicate by myself because both expressions have the same meaning as stated in the linked question. However, as the excellent answer provided by broccoli forest explains, there is a different nuance between them. This differenve is not explained in the linked question, therefore I think this question is not a duplicate but it is different from the linked one.

Answer

In short, 一人の～ sounds more specific and ～一人 more general. 一人の女性 often translates into "a certain woman".

1. 
   

   
   

   一人の女性を愛した男性

   
   

   
   
   


2. 
   

   
   

   女性一人を愛した男性

   
   

   
   

If I heard these phrases, I'd take #1 as "a man who loved (only) one woman" but #2 as "men who loved (only) one woman". That is because 一人の女性 probably means a specific woman, so I think that the man is specific, too. On the other hand, 女性一人 is probably unspecific, so I think that it is talking about a group of, or generally men each of whom loved a sole (but different) woman in his life.

Similarly(?), 三匹の子豚 reminds me of a fable about certain imaginary pigs and a certain imaginary wolf, but 子豚三匹 only of barbecue in your ranch.

Now, taking from the sample in the question you linked:

3. 
   

   
   

   一人の女性が生む子どもの数

   
   

   
   


4. 
   

   
   

   女性一人が生む子どもの数

   
   

   
   
   

In the original context, it talks about birth rate, thus I feel #4 is more preferable than #3 (though not ununderstandable). The reason is that the number is an average, while the number of children each actual woman has is very diverse and 一人の女性 cannot help but be related with a random woman. You can say "a whale is a mammal" to mean "whales are mammals", but replacing "women are shorter than men" with "a woman is shorter than a man" is weird, because obviously a certain woman is not necessarily shorter than a certain man. In this case, using 一人の～ with words that explicitly mean uncertainty (e.g. 平均 "average", 確率 "probability") makes it much better.