To put it simply, both useState and useEffect enhance functional components to make them do things that classes can but functional components (without hooks) cannot:

• useState allows functional components to have state, like this.state in class components.
• useEffect allows functional components to have lifecycle methods (such as componentDidMount, componentDidUpdate and componentWillUnmount) in one single API.

Refer to the examples below for further illustration:

useState

class CounterClass extends React.Component {
  constructor(props) {
    super(props);
    this.state = { count: 1 };
  }
  
  render() {
    return <div>
      <p>Count: {this.state.count}</p>
      <button onClick={() => this.setState({ 
        count: this.state.count + 1
      })}>Increase</button>
    </div>;
  }
}

function CounterFunction() {
  const [count, setCount] = React.useState(1);
  return (
    <div>
      <p>Count: {count}</p>
      <button onClick={() => 
        setCount(count + 1)}
      >Increase</button>
    </div>
  );
}

ReactDOM.render(
  <div>
    <CounterClass />
    <CounterFunction />
  </div>
, document.querySelector('#app'));

<script src="https://unpkg.com/[email protected]/umd/react.development.js"></script>
<script src="https://unpkg.com/[email protected]/umd/react-dom.development.js"></script>

<div id="app"></div>

useEffect

class LifecycleClass extends React.Component {
  componentDidMount() {
    console.log('Mounted');
  }
  
  componentWillUnmount() {
    console.log('Will unmount');
  }
  
  render() {
    return <div>Lifecycle Class</div>;
  }
}

function LifecycleFunction() {
  React.useEffect(() => {
    console.log('Mounted');
    return () => {
      console.log('Will unmount');
    };
  }, []); // Empty array means to only run once on mount.
  return (
    <div>Lifecycle Function</div>
  );
}

ReactDOM.render(
  <div>
    <LifecycleClass />
    <LifecycleFunction />
  </div>
, document.querySelector('#app'));

<script src="https://unpkg.com/[email protected]/umd/react.development.js"></script>
<script src="https://unpkg.com/[email protected]/umd/react-dom.development.js"></script>

<div id="app"></div>

Read more about useState and useEffect on the official React docs.

Your points are basically correct, some minor clarification:

useState is causing a re-render on the call of the setState method (second element in the array returned). It does not have any dependencies like useMemo or useEffect.

useMemo only recalculates a value if the elements in its dependency array change (if there are no dependencies - i.e. the array is empty, it will recalculate only once). If the array is left out, it will recalculate on every render. Calling the function does not cause a re-render. Also it runs during the render of the component and not before.

useEffect is called after each render, if elements in its dependency array have changed or the array is left out. If the array is empty, it will only be run once on the initial mount (and unmount if you return a cleanup function).

You can always check Hooks API Reference, which is a pretty solid documentation in my opinion