The Greek letter sigma (σ) has a different form (ς) when used at the end of a word. This distinction seems unnecessary to me, and it's not clear why it would emerge. Do we know why and when this distinction came to be? Was there a benefit for making this distinction? Does the evolution of the character or the literature explain how we ended up having two forms? This distinction seems to only appear in lowercase text, but I am not sufficiently familiar with the evolution of the Greek alphabet.
Thompson 1912 mentions the following on page 189:
Not a full answer but at least something to start with.
The oldest form of sigma is Σ, as found in inscriptions. In manuscripts, this was often simplified to the so-called "lunate" sigma, resembling the Latin letter C. (This is also found in Cyrillic).
When a scribe was writing connected script, the lunate sigma would be realized as σ, allowing the writer to continue to the next character without lifting the pen. At the end of a word, a small flourish was added to give ς.