It’s purely stylistic, but here are the rules - https://en.wikipedia.org/wiki/Long_s#Rules

Some of the rules for the use of the long s from https://en.wikipedia.org/wiki/Long_s

Long s was always used (ſong, ſubſtitute), except:

• Upper-case letters are always the round S; there is no upper-case long s.
• A round s was always used at the end of a word ending with ⟨s⟩: his, complains, ſucceſs
  • However, long s was maintained in abbreviations such as ſ. for ſubſtantive(substantive), and Geneſ. for Geneſis(Genesis).
• Before an apostrophe (indicating an omitted letter), a round s was used: us'd and clos'd.
• Before or after an f, a round s was used: offset, ſatisfaction.

It looks almost like the old german "S".

It was often used for "f" as well, specifically in print to save money.

Towards the end of the article, they explain the same thing was done with using "y" to replace the letters that make the "th" sound (ð and þ) so instead of "the" or "ðe" you got "ye"