It generally refers to the body size. A "Folk Guitar" will normally have a smaller body shape. I think it's a little smaller than an OM, but not really sure. Tone wise? Smaller guitars usually have less bass as compared to a Dreadnaught or Jumbo.
Yeah, the smaller bodies and folk shapes usually are more suited to fingerpicking than chordwork. They are very clear, and each string rings out very clear and quite bright. Great for fingerpicking and blues.
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Keep in mind that not all guitars that are called "folk guitars" are actually folk guitars. Sometimes it just refers to it's overall looks...etc.

I have a Yamaha FG735s that is referred to as a folk guitar but it's a dreadnought and is actually a bigger dreadnought than most guitars...bigger than martin and taylor and about the same size as a breedlove.