Absolutely no difference at all.

Want a shame and want a pity are both natural. They have not many differences.

Without thinking too hard about it, I would say there is little to no difference. If you ask a researcher they may be able to tell you how usage of the two varies.

Es importante señalar que "shame" y "pity" son cosas muy diferentes. Pero cuando se usan en estas expresiones, las frases tienen el mismo significado. Buena suerte! It is important to note that "shame" and "pity" are very different things. But when used in these expressions, the phrases have the same meaning. Good luck!

Thank you so much!! :D