Yep, same stuff. It's an organic acids naturally in grapes, but also a common ingredient in winemaking by itself or in a blend of citric and malic acids. This is one of the things that happens during aging and can be partially attributed to a "softening" of the wine, as the chemistry for whatever reason caused some of this acid to precipitate and fall out of solution. I've got a lovely zucchini wine (yes, really) that's full of them and looks a bit like a snow globe when you disturb the bottles.
When you open an older bottle of red, this is one of the things that makes up the sediment on the bottom of the bottle, among tannins and other anthrocyanins. Of course, the wine stains it red in this case. You should see the inside of a used wine barrel with all the build-up you can get!