Trying to use ONE button is WPF for 2 events.

<DockPanel>
        <Border Height="25"
                removed="SkyBlue"
                BorderBrush="Black"
                BorderThickness="1"
                DockPanel.Dock="top">
            <Grid>
                <Grid.ColumnDefinitions>
                    <ColumnDefinition Width="100" />
                    <ColumnDefinition Width="100" />
                </Grid.ColumnDefinitions>
              
                <Button x:Name="redBtn"
                    Width="100"
                    Grid.Column="0"
                    Content="RED"
                    Foreground="red"
                    Click="BoxClickHandler"/>

                    <Button x:Name="blueBtn"
                            Grid.Column="1"
                            Width="100"
                            Content="Blue"
                            Foreground="blue"
                            Click="BoxClickHandler"/>
   </Grid>
        </Border>       
        <Border Height="75"
                removed="SkyBlue"
                BorderBrush="Black"
                BorderThickness="1"
                DockPanel.Dock="top">
            <Rectangle x:Name="blueRedBox"
                           Margin="10,10,10,10"
                           Stroke="Red"
                           Width="60"
                           Height="60">
                <Rectangle.Fill>
                    <SolidColorBrush Color="Blue" />
                </Rectangle.Fill>
            </Rectangle>
        </Border> 
        <Border Height="25"
                removed="LemonChiffon"
                BorderBrush="Black"
                BorderThickness="1"
                DockPanel.Dock="Bottom">
            
            <Grid>
                <Grid.ColumnDefinitions>
                    <ColumnDefinition Width="115" />
                    <ColumnDefinition Width="150" />
                    <ColumnDefinition Width="100" />
                </Grid.ColumnDefinitions>              
                <Button x:Name="BlueGreenBoxColorChangeBtn"
                    HorizontalAlignment="Left"
                    Content="Change Color of Box"
                    Click="BlueGreenBoxColorChangeBtn_OnClick"/>

                <Button x:Name="CircleColorChange"
                    Grid.Column="1"
                    Content="Circle Color Change"
                    Click="BoxClickHandler" />

                <Button x:Name="ResetBtn"
                    Grid.Column="2"
                    Content="Reset"
                    Click="BoxClickHandler" />
            </Grid>
        </Border>     
        <Border removed="White"
                BorderBrush="Black"
                BorderThickness="1">
        </Border>
        <Canvas>
        <Rectangle x:Name="BlueGreenBox"
                   Width="145"
                   Height="126"
                   Canvas.Left="100"
                   Canvas.Top="25">
            <Rectangle.Fill>
                <SolidColorBrush Color="blue" />
            </Rectangle.Fill>
            <Rectangle.Stroke>
                <SolidColorBrush Color="Blue" />
            </Rectangle.Stroke>
        </Rectangle>
        <Ellipse x:Name="Circle" 
                 StrokeThickness="3"
                 Width="121"
                 Height="100"
                 Panel.ZIndex="1"
                 Canvas.Left="195"
                 Canvas.Top="30">
            <Ellipse.Fill>
                <SolidColorBrush Color="Green" />
            </Ellipse.Fill>
            <Ellipse.Stroke>
                <SolidColorBrush Color="Blue"/>
            </Ellipse.Stroke>
        </Ellipse>
        </Canvas>
    </DockPanel>
</Window>

using System.Windows;
using System.Windows.Media;

namespace DockPanels
{

    public partial class MainWindow : Window
    {
        SolidColorBrush greenBrush = new SolidColorBrush(Colors.Green);
        SolidColorBrush redBrush = new SolidColorBrush(Colors.Red);
        SolidColorBrush blueBrush = new SolidColorBrush(Colors.Blue);
 
      
        public MainWindow()
        {
            InitializeComponent();
        }

        private void BoxClickHandler(object sender, RoutedEventArgs e)
        {
            FrameworkElement feSource = e.Source as FrameworkElement;
            switch (feSource.Name)
            {

                case "blueBtn":
                    blueRedBox.Fill = blueBrush;
                    blueRedBox.Stroke = blueBrush;                   
                    break;

                case "redBtn":
                    blueRedBox.Fill = redBrush;
                    blueRedBox.Stroke = redBrush;
                    break;

                //case "BlueGreenBoxColorChangeBtn":
                //    BlueGreenBoxColorChangeBtn.Click += new RoutedEventHandler(BlueGreenBoxColorChangeBtn1);
                //    BlueGreenBoxColorChangeBtn.Click += new RoutedEventHandler(BlueGreenBoxColorChangeBtn2);
                //    break;

                case "CircleColorChange":
                    Circle.Fill = blueBrush;
                    Circle.Stroke = blueBrush;
                    break;

                case "ResetBtn":
                    Circle.Fill = greenBrush;
                    Circle.Stroke = blueBrush;
                    break;

            }
            e.Handled = true;
        }

        private void BlueGreenBoxColorChangeBtn_OnClick(object sender, RoutedEventArgs e)
        {
            BlueGreenBoxColorChangeBtn1();
            BlueGreenBoxColorChangeBtn2();

        }

        private void BlueGreenBoxColorChangeBtn1()
        {
            BlueGreenBox.Fill = greenBrush;
            BlueGreenBox.Stroke = greenBrush;
        }

        private void BlueGreenBoxColorChangeBtn2()
        {
            BlueGreenBox.Fill = blueBrush;
            BlueGreenBox.Stroke = blueBrush;
        }

        //public static readonly RoutedEvent BlueGreenBoxColorChangeBtn_OnClick = EventManager.RegisterRoutedEvent("BlueGreenBox", RoutingStrategy.Direct, typeof(DependencyPropertyChangedEventHandler), typeof(SolidColorBrush));

        //public event RoutedEventHandler BlueGreenBox
        //{
        //    add { AddHandler(BlueGreenBox, value); }
        //    remove { RemoveHandler(BlueGreenBox, value); }
        //}
    }
}