Final answer:
Home rule cities have autonomy detailed in charters, but are subject to state authority under Dillon's Rule; cities with independent charters may further define their governance structure and authority.
Step-by-step explanation:
Home rule cities are granted a level of autonomy that allows them some degree of independence from state government, typically detailed within a charter, resembling a state constitution's framework. The autonomy granted through home rule can be complex as states still retain certain powers over local governments under Dillon's Rule, which states that local jurisdictions exist at the pleasure of the state. Moreover, home rule may have limitations such as those cities with independent charters outlining their own local government structure and authority which can differ significantly from those prescribed by the state.