Either is fine. Club implies something smaller and more intimate (i.e. a book club, s sports club) while a society sounds larger (like something citywide).

When I was at university in England, I was for a time Societies Officer on the student union executive.  Most sports and hobby groups were called "clubs" e.g. Hockey Club, Chess Club; and most other interest groups were called "societies" e.g. Debating Society, International Society.  However, there was no rule.

The club should have a goal or an interest that unites the members of the club. The society is just a group of people without any restrictions about size, goal ... anything (world society, tribe society, family society, prison society). Every club is a society, but not every society is a club.