I’ll provide my view, as I use both sites (my askubu profile).
Ask Ubuntu is a Stack Exchange site (not a Ubuntu site), with Stack Exchange offering numerous Question and Answer sites; the AskUbuntu site is a site offering support for Ubuntu products/releases in standard support, with help provided by Stack Exchange users, plus some Ubuntu users who use the site as well. Ask Ubuntu is not a Forum, but Q&A.
Ubuntu Discourse (here) is a Ubuntu site; and is used by many different groups, originally not providing any support (that was offered at Ubuntu Forums), but now does allow support questions. Support is only a small part of what Ubuntu Discourse actually does. Ubuntu Discourse is also a Forum, and not a Q&A site, covering far more than the limited Q&A offered by AskUbuntu.
FYI: You may not see a difference between Q&A & Forums (as both are useful for support), but they do differ in approaches. Simply, on a Q&A site, you outline your single problem (question) and people write fixes (answers). Opinions & broad questions are off-topic on Q&A sites. If you do have a broad/complex question, you need to break it down into simple components, and then ask multiple questions on Q&A sites to fit within the rules. The Q&A rules aim in creating a database of simple problems & answers easy to be read later, being a benefit of Q&A format.