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What is the difference between those two KZG Polynomial Commitment Schemes?

Both represent the same thing. The first one uses the additive notation & the 2nd one uses the multiplicative notation. That is the only difference. KZG actually uses an Elliptic Curve Group, so ...
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2 votes

Pedersen commitments equivalence

An EC Pedersen commitment is of the form $C=(bG+vH)$, where $v$ is the scalar value being committed to, $b$ is the scalar blinding factor, and $G$ and $H$ are well-known generator points on the curve. ...
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How to multiply the Pedersen Commitment of two numbers?

Sort of related, we have the identity $$C(x_1*x_2,-b_1*b_2)=x_1C(x_2,b_2)-b_2C(x_1,b_1)=x_2C(x_1,b_1)-b_1C(x_2,b_2)$$ (note the similarity to the Diffie-Hellman identity) but in general we cannot ...
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