If you've used OnSong prior to 2019, you had purchased the app outright on the App Store. If you've never signed up for a subscription after that initial purchase, there is no on-going fee.
Some newer features and versions of OnSong are only available through an OnSong subscription. Also you can now subscribe through the App Store via an in-app subscription, or via the OnSong website via a Solo or Group subscription.
If you're unsure about the current status of your membership, open the Utilities Menu by tapping on the gear icon in the Menubar and then choose Account. You should then be signed in to view your account details. There you will see an Account row that describes your subscription:
Individual (AppleID) means that you have subscribed via the App Store with your Apple ID. You will manage your subscription through the App Store and all payments are made directly with Apple.
Individual (OnSong) means that you have subscribed to a Solo subscription through the website.
Organization Name (OnSong) means that you are a member of a Group subscription that has been setup and managed through the OnSong website.
If an arrow appears to the right of the Account row, you can tap to view other accounts that you belong to. For instance, you could have an individual/solo account that is subscribed, but also be a member of a group as well. OnSong automatically picks the account with the highest number of features that is not expired, but you can change the active account if desired.
Either way, you can tap on the Manage Your Subscription button to manage your subscription either through the App Store app or the OnSong website accordingly.