A sow is a female pig, which doesnt produce silk at all. Attempting to get silk from it would be difficult, if not impossible and futile. It wouldn’t matter how hard you try, you would get nothing.

You can get as much silk from a sows ear as you can get blood from a stone. I dont see much differnce, but i guess the sows ear phrase requires more culture context if it means “you can’t get something nice from rubbish.”