From the recent El Faro sinking post here on HN:

There's a General Alarm signal (above), but no Abandon Ship signal. The captain gives those manually.

(I may be blatantly wrong!)

To the best of my knowledge (not a sailor, but my work has netted me several hundred days on vessels offshore), 'Abandon Ship' is always an explicit, verbal order from the captain (or whoever follows him in authority if he is incapacitated)

The General Alarm typically calls for the crew to proceed (at haste!) to the muster station to be informed of the nature of the emergency and be put to work handling the situation.

Luckily, I've only ever had to abandon ship during a couple of drills.