I've never thought of the Ship's Carpenter as a variant of Pretty Polly, or vice versa. A woman gets betrayed and destroyed by her sometime lover, but that's about all the songs have got in common.

I suppose you could develop a song like Pretty Polly out of one aspect of the Ship's Carpenter story, but I've never seen any bridging versions to suggest that that is where it came from. It'd be interesting to know if there are any.