You're on wrong track. Props can be used either in stateful component or stateless component.
By meaning stateful component is not just for maintaining states
. Nor stateless component just for maintaining props
.
stateful !== states
stateless !== props
You can take this for short:
stateful <=> states <=> props
stateless <=> props <=> states
Where you can see (in short, there's more... look at the references), stateful component passes the states/props, the child component can use props, stateless component links props and hooks the states. - You might feel difficulty reading this line of statement.
Come back later after following the references to understand what I wanted to say, you'll obviously know what I meant for.
If you want to look about the differences between props vs state, then look at attached duplicate post:
What is the difference between state and props in React?
I would also suggest you to look at the docs about lifting state up.
Here's the link to the docs for props and states:
Components and props
State and lifecycle
By reading these references, you should have clear understanding of props and states.