...between Bath Shua - Judah's wife and the mother of his three sons, including Shelah - and Bath Sheba - King David's beloved and the mother of Shlomo Hamelach?

I don't recall anything.Bath Shuah is really, as far as I see, a very minor role in the Bible, with not much said of her in the written or Oral LAw (though I'm not an expert on Medrashim.)The Prefix BAth is really not so much to go on as a comparison. It's basically the female version of "someone of", which can refer to anything.

Rav Chaim, thank you for yor response. Of course, "Bath-Shua" means merely that she was the daughter of Shua and not much to go by for comaprison; what got me wondering was the fact that there is only one-letter differnece between the two names (patronyms?) Shua and Sheba. So I thought there might be some connection, especially considering that both women were related through marriage (love) to the same tribe. By the way, what happened to Judah's youngest son born by Bath Shua? Isn't his name somehow-or-other mentioned in Jacob's blessings?