Which is weir, because chicken is one of the few items in the grocery store that I haven't really seen a large increase in the price, and the all you can eat wings deals at restaurants have only slightly increased. Meanwhile, like you said, everything else that is chicken at a restaurant has noticeably risen.

So the brisket is generally an unappetizing piece of the cow corpse. A long time ago, some realized that slowly cooking it over a very long time, which has been 'formalized' into smoking it for 24 hours, makes the meat tender enough to eat. The brisket has different parts, some of which have more fat than others. The moist brisket is the portion where the fat is very thick. Generally the smoking process makes the fat shrink, but it's still a significant portion of the meat. Think a layer cake where the icing is give or take 1/6 - 1/4 of the cake's entire portion. That's moist.

The lean brisket is usually where either the fat was thin enough to not be visible after the smoking, or it was deliberately scraped off before/during the smoking. The meat will not be dry like a piece of toast, but you won't ever have a piece of fat in your mouth either. The way the particular bbq joint prepares it will differ, so assume these are broad strokes and not very specific designations.

Some people have preferences that are wild. My friend literally wants just the fat and will eat it like it's candy, while my mother wants it the consistency of jerky.