It seems to be the same data, at first glance at the least, but I guess your .gov.uk link is the authoritative base, from which other sites pull data.
https://find-and-update.company-information.service.gov.uk/officers/Pt7zKAA7fzLqJbJ77pn3yCCD60o/appointments
https://find-and-update.company-information.service.gov.uk/officers/9_JtS_IaTpZPYyNQtsQTefcMF6Y/appointments