I'm going to answer this myself, since I haven't seen good complete answers online. 助ける occupies a role overlapping with both word, which is particularly confusing for native English speakers, since the word encompasses "help," "save," and "rescue" depending on the context.

Previous answers on this site include this which just said that 救う is to rescue while 助ける is to help, which I don't think properly covers the nuance. Also there is this answer which compares 手伝う and 助ける and, conversely, says that 助ける means to save while 手伝う means to help. These are contradictory answers which don't really help learners grasp the nuance.