lstAnimals.ListIndex = 1

To tell which is the case, create a module-level Boolean variable m_MouseClicking. In the ListBox's MouseDown event handler, set this value to True. Check the value in the Click event handler. In the ListBox's MouseUp event handler, set this value back to False.

Private m_MouseClicking As Boolean

Private Sub lstAnimals_MouseDown(Button As Integer, Shift _
    As Integer, X As Single, Y As Single)
    m_MouseClicking = True
End Sub

Private Sub lstAnimals_MouseUp(Button As Integer, Shift As _
    Integer, X As Single, Y As Single)
    m_MouseClicking = False
End Sub

Private Sub lstAnimals_Click()
    If m_MouseClicking Then
        lblSource.Caption = "Mouse Click"
    Else
        lblSource.Caption = "Code"
    End If
End Sub