The letters are different. When I took German, 1954-57, all our reading materials were in fraktur (the old type often mistakenly called Gothic) and I had to learn to read it. The medial s is not crossed like the f; otherwise the letter shapes were identical.
Was it used in Latin? If so, then maybe they got it from Greek. If not, then it was probably their own invention.
It is not uncommon for letters in other alphabets to have a distinct final form. Hebrew has several letters that do. I have read that in Arabic, letters can have up to four different forms: initial, medial, final, and stand-alone. Even we, when handwriting use different forms of letters depending on the context. The r in or is distinctly different from the one in ar.