You are correct - only third-party, cross domain cookies. WSJ and other writers simplify to "cookies" because it's a simpler headline and only a small percentage of people understand the difference (even tech workers!). It's terribly annoying that they do this because first party cookies are invaluable and will never go away until there is something just as easy to maintain state on on a website (e.g. remembering that you're logged in from page to page, session to session).
Source - I work in marketing tech.