Wood engraving and woodcutting are part of the same family of printmaking, but are slightly different. The part of the wood that you carve is different. In woodcutting, you cut on the side of the tree, so basically perpendicular to the grain. In wood engraving, you engrave into the endgrain. It's like if you cut a tree down and made a block, you could see the grains, like the grains are pointing straight up.

You also would use two different types of wood. I can't remember the exact ones off the top of my head as it's been a year or so since I last truly sat down and engraved, but if I'm remembering correctly (and again, I could be misremembering) engraving requires woods like maple, not woods like pine. AKA, engraving uses hard wood, not soft wood like woodcuts. I learned to engrave with small maple blocks that were really high quality.

The way you cut/carve is different too. In engraving, you are literally shaving small bits of the wood away. I sometimes had to vacuum after a long engraving session because I had just tons of tiny shavings all over my desk, chair, and floor. Woodcutting is more similar to linocut and softcut cutting motions. The tools are quite different too. Instead of a U or V shaped tool, engraving tools are pointy, and the handle is round and fits quite nicely in your hand. The ones I used were Japanese. They are a bit hard to sharpen since if youre not perfectly flat when using a stone, it causes the flat of the tool to be rounded and can cause issues. They're very sharp, though, and the only time I ever got hurt was literally my very last engraving on the very last day of class, I poked myself in the thumb and was so mad about it. Not bad, but enough that it hurt, and a bandaid wouldn't stay because it was at the end of my thumb.

Wood engravings are also usually smaller, because it's more intense, more detailed, and way more expensive than woodcutting. There's very few people in the world who still make blocks for engraving, and while they're very skilled, it can get pricey. We had to order ours in a class set and once we ordered, we couldn't get new ones because of price and shipping times. Woodcutting can be done on bigger blocks and is cheaper since you can use softer, more common woods. Wood engraving is easier to do in tandem with letterpress printing, however, as blocks for engraving are type-high (0.918 inches!). I personally have printed my own engravings alongside hand set type on Vandercooks, which allowed for much faster printing since I didn't have to swap everything out and line everything up to print a new layer.

Engraving came later, roughly the 15th century if I've got my dates right, while woodcutting is from China. I've seen dates ranging from the 200s BCE to the 200s CE to the 700s CE, so basically it's really old. Just like printing presses! East and Southeast Asia has had them for centuries before Germany brought them to the rest of the world.

I probably missed some stuff, but that's the basics from someone who at least studied one of the two things you're asking about. If you'd like to see more, there are a bunch of presses and blogs online actively engraving or cutting, and they usually each have a small blurb or a post explaining the differences or basics. If you're looking to collect prints, the Wood Engravers Network is a wonderful resource, and you get basically random prints from very very incredibly skilled engravers if you become a member, plus a newsletter.

Mexico City streetstyle by Maurycy Gomulicki