Flutter Test Widgets find.byType(TextField) Works, find.byWidget(TextField()) Doesn't work. Why?

I am just getting started with flutter widget testing and came upon this issue. I was wondering if this is expected behavior. When trying to find my TextField with find.byType it succeeds but with find.byWidget it doesn't. Is this normal or am I doing something wrong? The goal is later to enter text in the textfield and tap a button after.

My textField and button:

Column(
    children: [
      TextField(
        style: TextStyle(
          color: Colors.black,
        ),
        autofocus: true,
        autocorrect: false,
        enableSuggestions: false,
        controller: _controller,
        cursorColor: Colors.black,
        decoration: InputDecoration(
            hintText: 'Fill in.....',
          hintStyle: TextStyle(fontSize: 18),
        ),
      ),
      Row(
        mainAxisAlignment: MainAxisAlignment.end,
        children: [
          ElevatedButton(
              onPressed: () {
                onSubmit(_controller.text);
              },
              child: Text('Press me!',
                  style: TextStyle(
                    fontSize: 18,
                    color: Theme.of(context).primaryColorBrightness ==
                        Brightness.dark
                        ? Colors.white
                        : Colors.black,
                  ))),
      ],),
    ],
  ),

And this is my test:

tester.ensureVisible(find.byType(TextInputWidget));
  expect(find.byType(TextInputWidget), findsOneWidget);

  final a = TextField(
    style: TextStyle(
      color: Colors.black,
    ),
    autofocus: true,
    autocorrect: false,
    enableSuggestions: false,
    controller: TextEditingController(),
    cursorColor: Colors.black,
    decoration: InputDecoration(
      hintText: 'Fill in.....',
      hintStyle: TextStyle(fontSize: 18),
    ),
  );

  //expect(find.byWidget(a), findsOneWidget); // Fails
  expect(find.byType(TextField), findsOneWidget); //Succeeds

Parts of your test are missing, but it looks like you are trying to find widget a in your tester where it is not known. If you want to find a widget by its variable reference, you have to use the same reference when you define the widget that is then passed to pumpWidget() method like so:

final a = TextField(...);
tester.pumpWidget(Container(
  child: a,
));
expect(find.byWidget(a), findsOneWidget);