Question: Is white vinegar, aka the stuff just labelled as "vinegar" in the US and which I use for cleaning my kettle, the same as "White wine vinegar", which I have purchased on accident a time or two? If not, what is white vinegar made of?

Answer: 
White wine vinegar is a completely different thing, it's less tangy and is more diluted as it's made from the white wine. The Ethanol in the white wine is let to oxidise into ethanoic acid, which is a carbolyxic acid also known as vinegar.
They are different. You can drink white wine before it turns to vinegar but if you drink distilled water and acetic acid you’re nuts.