I don't know why Microsoft is firing a MouseMove after a click, whether its is by design or just a bug.
But you can ignore it in your code by setting a flag in the click handler and testing it in the mousemove handler.
Private Sub Form1_MouseMove(ByVal sender As Object, ByVal e As System.Windows.Forms.MouseEventArgs) Handles MyBase.MouseMove
If bIgnoreMouseMove Then
bIgnoreMouseMove = False
Return
End If
Console.WriteLine("Form1_MouseMove")
End Sub
Private Sub Form1_Click(ByVal sender As Object, ByVal e As System.EventArgs) Handles MyBase.Click
Console.WriteLine("Form1_Click")
bIgnoreMouseMove = True
End Sub