One-time signup (initiation) fee / account creation fee
This is a fixed cost you pay only once, when you join. It covers administrative overhead: creating your account, orientation, maybe issuing a membership card, paperwork, etc. In your case, $100.
Recurring membership fee
This is what you pay monthly to get “unlimited” access. “Unlimited” means no cap on how many classes / sessions you can attend (within the gym’s schedule).
No-contract