Question

What is the use of the Style tag between Button.Style and Style.Trigger? Is it because Style an attached property?

<Button.Style>                
    <Style >
        <Style.Triggers>
            <Trigger Property="Button.IsMouseOver" Value="True">
                <Trigger.EnterActions>
                    <BeginStoryboard>
                        <Storyboard>
                            <DoubleAnimation From="1" To="15" Storyboard.TargetProperty="FontSize"></DoubleAnimation>
                        </Storyboard>
                    </BeginStoryboard>
                </Trigger.EnterActions>
            </Trigger>
        </Style.Triggers>
    </Style>
</Button.Style>

Answer 1

This is what the XAML what look like in code:

var button = new Button();
button.Style = new Style();
button.Style.Triggers.Add(new Trigger() ...);

The tag <Button.Style> references a property on Button and with the <Style> tag you are setting the style property to an object of type Style. If you had a derived class for Style, such as MyStyle, then the XAML would look like this:

<Button.Style>                
    <local:MyStyle>
    </local:MyStyle>
</Button.Style>