The original version of your last method (pre-Edit) will return all different sorts of colors. I would be sure to use a single Random object rather than create a new one each time:
Random r = new Random();
private void button6_Click(object sender, EventArgs e)
{
pictureBox1.BackColor = Color.FromArgb(r.Next(0, 256),
r.Next(0, 256), r.Next(0, 256));
Console.WriteLine(pictureBox1.BackColor.ToString());
}
It produces all sorts of different colors:
Color [A=255, R=241, G=10, B=200]
Color [A=255, R=41, G=125, B=132]
Color [A=255, R=221, G=169, B=109]
Color [A=255, R=228, G=152, B=197]
Color [A=255, R=50, G=153, B=103]
Color [A=255, R=92, G=236, B=162]
Color [A=255, R=52, G=103, B=204]
Color [A=255, R=197, G=126, B=133]