Essentially, Yes. The other stories were abandoned.
On that famous night, there were four people trying their hands at ghost stories: Lord Byron, Percy Shelley, his wife to be Mary Godwin and John Polidori who was not known as a writer but was serving as Byron's physician.
We won't go over the genesis of Mary's tale, Frankenstein, as this is well known.
Byron was unsatisfied with his effort, a tale about Vampirism, and abandoned it. It was later appended to one of Byron's poems, Mazeppa, by its publisher John Murray without Bryon's approval. Byron was not happy:
I shall not allow you to play the tricks you did last year with the prose you post-scribed to 'Mazeppa,' which I sent to you not to be published, if not in a periodical paper, – and there you tacked it, without a word of explanation, and be damned to you.
This story became variously known as Fragment of a Novel, A Fragment and The Burial: A Fragment.
Polidori also began and abandoned a story. Mary Shelley recalled:
Poor Polidori had some terrible idea about a skull-headed lady, who was so punished for peeping through a key-hole — what to see I forget — something very shocking and wrong of course; but when she was reduced to a worse condition than the renowned Tom of Coventry, he did not know what to do with her, and was obliged to despatch her to the tomb of the Capulets, the only place for which she was fitted.
However, Byron's fragmentary tale also inspired him to begin work on his own Vampire story, which he went on to complete at the urging of a friend. It's worth noting that the relationship between Polidori and Byron was fraught, and it's possible that the novel is also meant as a metaphor for the strains Byron put upon the physician, "sucking" the life out of him.
That manuscript lay forgotten for three years and was then discovered and published by journalist Henry Colburn who published it as The Vampyre without Polidori's permission, in fact attributing it to Byron. Polidori fought to reclaim his attribution but eventually fell into depression and died at the age of 25, possibly by suicide.
Shelley, apparently, tried to write something inspired by his childhood but was first to give up the task. As a poet, he struggled to write fluid, engaging prose. Instead, he spent the time encouraging Mary's effort. She recalled:
Shelley, more apt to embody ideas and sentiments in the radiance of brilliant imagery, commenced one founded on the experiences of his early life.
This unsatisfactory manuscript was, presumably, lost. There is not further mention of it in any of the sources I could find.
- The Works of Lord Byron: Embracing His Suppressed Poems, and a Sketch of His Life. Boston: Phillips, Sampson and Co., 1854, p. 897.
- Shelley, Mary. Frankenstein. Author’s Introduction to the Standard Novels Edition. OneWorld Classics. 1818 (last ed. 2008).
- Polidori, John William (2009), Rossetti, William Michael, ed., The diary, Cornell, NY: Cornell University Library