UK vs. American terms for furniture restoration/refinishing supplies?

I’m reading a book written in the UK on furniture restoration. It’s an informative and fascinating read. However, I live in the US, and you guys apparently have a completely different hardware store than I do. ^_^

What the heck is “meths”? and what is “white spirits”?

I use mineral spirits and paint thinner regularly… I’m assuming that’s what the above UK terms refer to, but which is which?

And is a “burnisher” a wood file?

“Wire wool” = “steel wool”, right? Just like cotton wool = cotton balls.

…...I think that’s it.

Help?