2 Buck Chuck is not TJ's house brand but a wine made by an individual company that is not Charles Shaw. Here is an excerpt from an article about 2 Buck Chuck.
There's also the story that Charles Shaw is a bighearted billionaire who wanted to expose the proletariat to the finer things in life.

Actually, it's an over-abundance of grapes that's made Charles Shaw cheap to bottle -- an estimated 5 million cases so far. It's easily outselling more famous brands like Mondavi and Gallo in California.

And Charles Shaw?

It's a wine label owned by Fred Franzia, a distant relative on the Gallo family vine. He's a reclusive businessman considered a pain in the neck to California's wine establishment.

Franzia controls scores of brands and labels including Charles Shaw that under-sell the prestige vineyards. And "Two Buck Chuck" is just his latest broadside: "We have others up our sleeve we think are even better coming out."

He also controls more than 30 square miles of California vineyards. And he thinks big. Next he plans to take on invading Australian wine makers.

"We're going to take 'em on. Slap 'em around as hard as we can!" he said.

Yes they do make white wines but they are not nearly as good as the reds. To me they taste like Panther Piss.