What is the relation between stateful and stateless widgets in Flutter?

Question

A stateful widget is defined as any widget which changes its state within its lifetime. But it is a very common practice for a StatelessWidget to have a S

Answer 1

Answer for the Stack Overflow question - statefulness vs statelessness.

In Flutter, the difference is that stateless widgets can be defined by all the constructor arguments alone. If you create two stateless widgets using the same arguments, then they will be the same.

A stateful widget, however, is not necessarily the same as another built with the same constructor arguments. It might be in a different state.
Actually, a stateful widget is immutable (stateless) itself, but Flutter manages a separate state object and associates that with the widget, as explained in the StatefulWidget doc. This means that when Flutter rebuilds a stateful widget, it will check to see if it should reuse a previous state object and will, if desired, attach that state object to the widget.

The parent widget is stateless because it does not care about its child's state. The stateful child itself (or technically Flutter) will take care of its own state.
On a high level, I agree that this makes the parent widget stateful, because two parents might contain two childs with different states and thus be technically different themselves. But from the viewpoint of Flutter, it builds the parent widget without caring about the state and only when building the child will consider its statefullness.