They both state the same thing, concealed...that is whatis prohibited...if you have a LTC you will be good to ccw. I don't understand your confusion on "about his person" and then asking if it would apply to an un-concealed weapon? The phrase "about his person" would be within arms reach and concealed, say a back pack or a saddle bag on a horse. Does this clear it up?
I hope this helps and don't consider this legal advice.