Mentions, mostly. You can't receive a direct message from someone you're not following (I think?)

Harassers tweet replies to every tweet you make – always adding a bit of twisted rethoric that makes them sound more reasonable than you, and discredits what you say. All of which your followers will see if they click to look at the "conversation" about your tweet. It's all public.

The effect, on Twitter, is that they drown the more infamous threats in a mob of people who slowy come into the conversation from believing the sneaky rethoric (and false info, often) is the whole story. It's basically the opposite of smashers/rioters joining a peaceful protest. They build the protest around themselves and use the protesters to reinforce their lies and claims to legitimacy.

You can disable notifications for non-follower mentions and such (only for yourself), but people can infinitely create new accounts, for which the default setting is always that everyone will see their tweets and replies.

Blocking is agressively an opt-in, per-user feature. And again, the default is a completely public status. Everything you might have blocked becomes visible if you visit your Twitter page and aren't connected. It can really break a person down.