Plan groups organize plans. And plans define the payment cycle via its periodicity.
All Plans are bundled into a parent Plan Group. Plans cannot exist outside of plan groups, and each plan can only exist inside of a single plan group.
An account can only see the sibling plans of its plan group. When an account starts a subscription, a cached copy of the plan group, the selected plan, and all sibling plans, is created inside of the subscription itself. On the account management page, only the plans in that cached list will be available.
This means that you can change the price, or entitlements, of an existing plan without impacting existing subscriptions. By default, changes to a plan do not change existing subscriptions. However, there are flags in those API calls that will let you propagate those changes to active subscriptions.
The frequency and payment amount are determined by the plan's Periodicity.