Yes, the term "resaw" was confusing to me at first too.
"Resawing" refers to a method of cutting the wood. It basically means a ripping cut, but through the thickness of the board, rather than the width of the board.
For instance, you might resaw a 1"x8" into two 3/8"x8" pieces of wood. A typical ripping cut might turn a 1"x8" into two 1"x3 15/16" pieces of wood.
Resawing is generally done with a bandsaw because the height capacity is greater than other machines. However, it's also possible to resaw using handsaws, and even a tablesaw (though you might have to finish the cut using a handsaw if the board is too wide).
They're both bandsaws... but resaw the noun versus resaw the verb are different.
Technically speaking, it means "To saw again." Duh, right? There's some truth to it, though. When you get lumber from a mill, it's sawn to a certain thickness. If you want to use thinner stock, you can either plane it down, or saw it again to the thickness you want. That's where the word comes from. Using a bandsaw is one of the most common ways of resawing.
A bandsaw designed for the purpose of resawing. They usually take HUGE blades that are very thick. VERY thick. Like ... 3-4 inches thick. BIG blades. They usually have quite a bit of height capacity as well, since the thicker you can saw, the wider your veneer, etc. They also have huge motors to power through the thick stock.
The basic rule is "all resaws are bandsaws but not all bandsaws are resaws". A resaw is a very specific application of the bandsaw. You can usually use some of the larger bandsaws to perform the act of resawing using the widest blade that will fit on the saw safely.
"Re-Saw" bandsaws usually refers to the big boys. Usually built for commercial operations. Saw mills sometimes cut large slabs, on their big saw and then cut "Lumber" on a smaller re-saw. They can be either vertical or horizonal.