This essay explains a useful point:

‘Forebitters were not work songs. They were songs of the sea that were sung for entertainment purposes only. Crew members would sing forebitters during the dog-watches: the times of the day when they were involved in solo deck duty, such as emergency lookouts. … such songs were called ‘fore-bitters’, because they were sung round the fore bitts [big strong fittings used to secure anchor and mooring lines – Ed], or they were called ‘come-all-ye’s’, because so many began with the words “come all ye sailormen.”

‘These songs were also sung in the forecastle, or as shellbacks referred to it as, the fo’c’sle which were the men’s living quarters below deck.

‘A simple clue that a song is a just a song of the sea and not a sea shanty is its length and lack of a short call and response form. “Although these [forebitters] are now often grouped together with shanties by enthusiasts, a sharp distinction existed between these leisure-time songs and sea shanties in the life and mind of a
sailor”.’

So: shanties are work songs, like agricultural and railroad building work songs. Forebitters are sung at leisure – and the ones I know (which are quite numerous!) have all sorts of functions and themes, such as warning about the way sailors get treated ashore or on particular ships.

I have to say I like a good story – and so forebitters are often more my thing!