Puedes hacerlo manejando los eventos correctos:

En VB:

    Private ReadOnly State_Normal As Color = Color.Gray
    Private ReadOnly State_Focused As Color = Color.White
    Private ReadOnly State_Clicked As Color = Color.Red
 
    Private Sub Button_MouseEnter(sender As Object, e As EventArgs) Handles Button1.MouseEnter
        sender.backcolor = State_Focused
    End Sub
 
    Private Sub Button_MouseLeave(sender As Object, e As EventArgs) Handles Button1.MouseLeave
        sender.backcolor = State_Normal
    End Sub
 
    Private Sub Button_MouseDown(sender As Object, e As MouseEventArgs) Handles Button1.MouseDown
        sender.backcolor = State_Clicked
    End Sub
 
    Private Sub Button_MouseUp(sender As Object, e As MouseEventArgs) Handles Button1.MouseUp
        sender.backcolor = IIf(sender.focused, State_Focused, State_Normal)
    End Sub
 

En C#

        private readonly Color State_Normal = Color.Gray;
        private readonly Color State_Focused = Color.White;
        private readonly Color State_Clicked = Color.Red;
 
        private void button1_MouseEnter()
        { button1.BackColor = State_Focused; }
 
 
        private void button1_MouseLeave()
        { button1.BackColor = State_Normal; }
 
 
        private void button1_MouseDown()
        { button1.BackColor = State_Clicked; }
 
 
        private void button1_MouseUp()
        { button1.BackColor = (button1.Focused ? State_Focused : State_Normal); }