Is donating a small sum to a Hebrew free loan society considered the mitzvah of tzedekah or the mitzvah of giving a loan?
Essentially it is the mitzvah of giving a free loan, however if the person getting the loan is poor it would also be included in If the money is loaned to a poor person (See Y:D 149-6, Ahavas Chesed 18).
As a side point, the Chofetz Chaim (Ahavas Chesed) writes that a person should divide his maaser money, and give 2/3 to tzedakah, and 1/3 to gemach. His reason is because each of the two has it’s own unique benefit. The tzedakah is considered a full chesed, because the poor person doesn’t have to give the money back, however with a gemach the money has to be returned. On the other hand when a person gives to a gemach, the money is like reusable mitzvos, the same money will do multiple mitzvos.