ASTM is the American Society For Testing And Materials. They test the materials to ensure that they are reliable - or something like that. I don't know exactly what ASTM is or does, but that's my general idea.
And this is BETA: BETA Safety - Body & Shoulder Protector Standard Explained
They are two seperate testing societies I believe.
The Rhodney Powell are BOTH ASTM approved and meet BETA Level 3 safety standards. Same with the Flex Rider. I am not sure about the Aerowear. The Inflatable vest also.
Tipperary - meets NEITHER ASTM or Beta levels of safety standards / approval.