I titled a short story "The Girl without a Soul". But recently I've been thinking on naming it "The Girl who didn't have a Soul."
Do they mean exactly the same thing? Is there an advantage to using one over the other? As a short story title, what impressions will readers get when they see the different titles?
Yes, they mean exactly the same. There are plenty of stories that have "who didn't have" in the title; and it really doesn't connote an event in the past. By contrast, Amazon has no fiction books with "who doesn't have" in the title.
It's very common to use the past tense in the title of a story, without any implication that something happened in the past, or that something is not happening in the present.
To answer the second question, "The Girl without a Soul" flows better in my opinion. "The Girl with no Soul" is better still.
This may seem like a trivial distinction, but as a title choice it's important as the title conveys an overall sense of the tone of the story.
First of all, the use of the contraction didn't is less formal than without so it might be best to consider the verbiage you've used throughout the story and match the word choice to the formality of the voice in the story. Next, "without" is more concise as it's a single word, and can't is a contraction of two words plus requires the use of "have". If your language is meandering in the story and not overall concise, to show your reader that you would maybe consider can't.
Now that the technical differences are spelled out, without conveys an absence of a soul, when I hear "without a soul" I think of a void, of absence and of longing, and seems more wistful of the two, whereas "didn't have" seems less of a statement of absence and void and more a statement of loss. None of that is specifically spelled out by the definitions, this is more of a connotative distinction and more of a conveyance of the unspoken feelings the words conjure. If the story is more about loss, maybe "didn't have" is better, whereas if the story is about absence, a void and of longing, it seems that "without" would be a better choice. Didn't have also seems like it has more of a 'concrete' or definite feeling, as opposed to the wistful ethereal feeling conveyed by without. Again, pick the choice that is more in line with the words you've used in the story.
Finally, and maybe the most important consideration, "didn't have" is past tense while "without" is present. If the girl gets a soul later in the story, it may be more apropos to use "didn't have", or another synonymous past tense phrase, if she doesn't get a soul, it might be a better idea to use "without". That said, if your style is to withhold clues from the reader about the ultimate end of the story rather than try to let them guess at your intention, reverse that advice.
Hope this helps!
"The Girl Without a Soul" scans better, because it comprises three pairs of unstressed-stressed syllables. "Who Didn't Have" does seem more childlike, so might be appropriate if you imagine the title being spoken by the child's peers.
To your second question first, because it's easier, "The Girl Without a Soul" would definitely sound better as a title of a story.
These two phrases do not mean the same.
"The Girl who didn't have a Soul" sounds like a story about a Girl who once did not have a soul, but may have one now. This phrase emphasises the fact that the Girl had no soul in the past.
"The Girl Without a Soul" sounds like a story concerning a girl without a soul, and implies that this is the case throughout the whole story. It does not give the impression that the Girl will, at the end of the story, have a soul.
However, the difference between these two statements are so slight, to dwell in them would be pedantic. Based on how your story goes, you could choose either statement. However, "The Girl without a Soul" does sound better.
