Weak and strong equivalence principles

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Hello,

I would like to see more clearly the differences between the various forms of the equivalence principle.
When reading about it on http://en.wikipedia.org/wiki/Equivalence_principle" I have the strange feeling that the difference is too small and too easily accepted to justify the difference in their names as "weak" and "strong".
In addition, I guess that on the experimental side it make really a difference.

As a side topic, I would also like to understand more clearly where and why which version of the EP has been used and was necessary in building the theory of General Relativity. My background on that is rather naïve: since acceleration changes the metric tensor so should gravity also change it. And for the rest I take GR as a beautiful mathematical construction that expands on the idea that gravity is geometry.

Could you help me clarify this, by your sharp explanations, or by excellent references.

Thanks a lot,

Michel
 
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Please explain to me your understanding of the two forms of the equivalence principle.
 
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