Hi Doc. This looks to be a 9 year old post from the dates. It's been brought back up a few times, including now. Just saying that, as you may not get a reply from the OP (Original Poster). Some of the names here are not familiar, and some are of folks who we no longer see.
I'm certain that yes it is a bandsaw box, and a fairly basic one. I'm just starting out on a journey to make some, and if you are on Facebook I'd suggest looking into the group I like there for current info on all things bandsaw box. It's the "The Alex Snodgrass Bandsaw Boxes Community"
https://www.facebook.com/groups/1578881979036037
Every day brings in new info, and there are a ton of active makers, who post recent work, and some great pics, and Ideas. I have to admit to being a Facebook newbie, and am not real familiar with all of it's features, but yesterday I figured out "FILES" and some users have posted usable files for designs, a few that I am interested in making.
I want to make a few of the Cracked top boxes, they had several sizes. An 8" tall, and a 12" tall, either of which could make a nice first jewelry, or "things" box for either a young girl, or boy, and I'm pretty sure they would like the look. Unfortunately both of those are .pdf files, and you cannot post them here, and attempts to make them a jpg file don't work. So I can't post them here.
They did have a generic file for the boxes though, that was a .jpg it's below. Versus the 8, 10, and 12" they had it appears this as is, would make about a 5" or 6" tall box. I suppose you could blow it up, hopefully without too much distortion, but the larger ones they have there do seem a better size. Most people making these are using an 1/8" or 3/16" blade due to the radius's Seeing that Alex is involved a LOT of them are also using Carters small blade guides on their saws as well. Having one I can attest they do turn a double sided guide, into something like a Ferrari, as far as turning radius. But they only work on the smaller blades. If anyone wanted one, and wasn't sure which of the many to get? I would suggest contacting Carters Customer service, and they could get you the correct one for your model of bandsaw. Not cheap, also not real expensive, but guaranteed to make a change on your ability to make close curves on a bandsaw.
I also got a double heart pattern that is also a ,jpg A lot of people do these on a stand by just tilting it to the left a tad, and it makes contact on the point, and the curve on the left side
These are just a few of the ones they have, like I said every day brings a number of new boxes, and ideas for them. Alex is very present in the groups day to day, and some of the others in the group are bandsaw box guru's. A very helpful group, and looking at questions a lot of people seem extremely happy to be a part of it. I know I am, but I've been an Alex fan for years, and later this month have 2 classes set with him at my local WoodCraft. A bandsaw box overview class, and a 3D cutting board, which I have done in the past, but mine was all TS. Alex only uses a bandsaw, so just to see how that works I am gonna go do a looksee, @@.
As far as finishing? What I can tell you is there is a TON of really fine grit sanding involved. You don't want to narrow any of the parts too much, so a lot of sand, sand, sand, but very fine grits so you don't make an XXXL size a medium in a few swipes. Some of the really cool boxes have a width not much wider than the blades kerf, and pulling drawers open is like a vacuum.
I'm currently in practice mode, and am finding it best to glue up chunks of crap leftover pieces of 2 x 4 and such, and using them to get the cut shapes, and sequence down on the junk wood, rather than burn up a lot of good wood learning. There is some learning curve to it, and I'm a lot more of a re-sawyer, than a curve cutter, so different hand eye stuff. Plus tons of backing out of cuts. I suggest to turn the saw off, let the blade stop, and THEN pull out. Not to there is a 50/50 chance of barking your cuts, and then you have a nice thin line, and all of a sudden, Grand Canyon. I haven't seen an instance yet where the back slab didn't come off first, then you do your entry cut, and go about tracing your inner pattern. Most of them take off about 1/4" for the back, or just less. Same process for each drawer. Really isn't rocket science, but it is a world of fun.