Public fundraising lets startups tell the general public they're raising money—on Twitter, Facebook, blogs, TV, advertisements, wherever. The legal term for public fundraising is ‘general solicitation’.
Startups can only accept money from accredited investors whether they raise money publicly or not. However, startups that raise publicly are required to verify that each of their investors is accredited.
If a startup that raised publicly closes their round on AngelList (via syndicates), AngelList will handle all 506c investor verification.