Sappho’s poetry is conventionally referred to by number, rather then title or first line. Because the ancient edition of her poetry does not survive, there is no canonical ordering for the poems and thus there are various different numbering systems. In 1955, Edgar Lobel and Denys Page produced a scholarly edition of Sappho and her contemporary Alcaeus, and modern scholarship has largely used their numbering system ever since.
For ease of reference, this site uses David A. Campbell’s numeration in Greek Lyric I: Sappho and Alcaeus (1990) as its primary numbering system. This is an updated version of Lobel & Page’s system, incorporating scholarship and new discoveries for the thirty years after their edition was published. Where a text is not included in Campbell but is in the more recent edition by Camilo Neri, Saffo, testimonianze e frammenti: Introduzione, testo critico, traduzione e commento (2021), this is noted as e.g. "fr. 243A Neri".
This balances the competing needs of using a modern standard which includes all of the most recent discoveries, with using an edition which readers of this site might reasonably have access to: Campbell’s edition is affordable, widely available, and comes with introductory material, translations, and notes in English; Neri’s is none of these things.
Where I discuss a translation which uses a different system of numeration, I give the standard numeration first and that translation’s equivalent afterwards, thus: “fr. 1 (38 Barnard)” for the poem which is fr. 1 in the standard edition.
Broadly speaking, the Lobel–Page system and those based on it try to organise the poetry of Sappho as it would have appeared in the ancient Alexandrian edition. Thus the poems from the first book are numbered frr. 1–42 (with fr. 1 being the poem which was at the beginning of that book), followed by the rest of the poems which can be assigned a specific book in the ancient edition. From fr. 118 are those which Lobel and Page could not assign to any specific book of the ancient edition; from fr. 169 to fr. 192 are individual words quoted by ancient authors without further context.
Frr. 193 onwards are extracts from ancient authors which discuss Sappho or her poetry but do not clearly quote any of her words.