I think a very defining difference is that the “Hechsher Tzedek” does not involve itself in any Kashrus issues. Therefore what they are doing is coming up with an alternative definition of Kashrus (and a subjective one at that).
They aren’t trying to redefine kashrus, one of the prerequisites for the Hechsher Tzedek is that the product also have a Kashrus Hechsher. What they are doing is repackaging “western values” (based on their secular philisophy) as jewish values under the guise of “Tzedek”.