To me, a "spank" is usually a mild to moderate slap on the rear, a part of the body particularly well cushioned that can handle it just fine without physical trauma, not to mention psychological trauma.
When I think of a child who has been "beaten", I imagine repeated bludgeoning across the body, often with a tool, and usually with visible bruising and possible laceration and bleeding.
"Spanking" can definitely include implements, though that's less common nowadays as people have started to view the act in a less positive light overall.
And the "without psychological trauma" is one aspect where it isn't really that clear if there is a level of spanking that avoids that whole issue.