Lambdas in java: variable vs class field [duplicate]

Variables in lambda`s must be effectively final. Ok. But why it is allowed to assign class field value in example code below?

Does heap and stack cause this difference? Why?

class Scratch
{
    public String field = "class field";


    public void example()
    {
        Function<String, Integer> funcWithField = s ->
        {
            field = "New field value from lambda";
            // IT`s OK here
            return field.length();
        };

        String variable = "var";
        Function<String, Integer> funcWithVariable = s ->
        {
            // Though such things are restricted!
            // variable = "some other loooong value for variable";
            return variable.length();
        };
    }
}