No one before really said it, but the acronym “W3C” generally refers (and should always refer) to this site: https://www.w3.org/. The W3C is one of the official organizations that sets standards for the modern Web, and should absolutely be considered an “authority” because they help to define the standards.
W3C does not, and should never, refer to this site: https://www.w3schools.com/. I’m not even sure where people get the idea that it does because there’s no “C” in their name.
As has already been pointed out, the two sites are not affiliated with each other. That previously-linked course on edX is by the W3C. Not W3Schools. So that course can be considered to have reliable and definitive information. The certificates on W3Schools, however, are just random certificates on a random Internet site—i.e., they’re basically worthless and not worth paying money for.
The title of this thread should be changed because it contains potentially misleading information. The W3C has and never will offer any kind of certifications.