Does using "among them" or "including" in a list of items indicate a comprehensive, or partial, list?

I’m trying to figure out if using "including" or "among them" in the following sentence suggests that the examples listed are comprehensive, or whether it suggests that the examples given are only a partial accounting.

This is the sentence: "The Foundation allocates $500,000 in combined aid to education charities, among them Charity A and Charity B."

Alternative: "The Foundation allocates $500,000 in combined aid to education charities, including Charity A and Charity B."

Does either sentence suggest that Charity A and Charity B are the only ones jointly getting $500,000 in support from the Foundation? Or does it indicate that the two charities are among a broader cohort of charities that each gets a part of that $500,000 in support (and that the other charities that receive a part of that support just aren’t listed)? Thank you.