The boxes for Japanese pots can vary all over the place. To lay out the general scenario.......
There can be no box at all.
The box can be of cardboard and have a printed label with typeset type.
The box can be of cardboard and have a caligraphic looking but printed label.
The box can be of very inexpensive wood construction and have no labeling at all.
The box can be of inexpensive construction and have black caligraphic writing on it and a red stamp (or two). This writing could be done by a distributor, the vendor, or the artist.
The box can be of good quality construction and have black caligraphic writing on it and a red stamp (or two). This writing could be done by a distributor, the vendor, or the artist.
The box can be of good quality construction and have black caligraphic writing on it and a red stamp (or two). This writing is done by the artist or someone on his/her staff designated by the artist to do so.
The box can be of both superior quality wood and construction and have black caligraphic writing on it and a red stamp (or two). This writing is done by the artist.
You can put in there some other permutaions of this idea... but that is the general "heiarchy" of things. In larger operations sometimes the caligraphy on the boxes for the lower bracket works is done by the deshi or shokunin or office workers. Maybe the master potter only affixes the hanko. For lower priced works, sometimes there is an extra charge for adding the "artist signed box", due to the time and costs involved on a piece that does not carry support for that in the original price.
Generally speaking, the "increasing" heiarchy above goes hand-in-hand with increasing price for the work. One way to potentially jack up the percieved value for a piece is to add in a wooden box to it. Wooden boxes are traditionally reserved for the "better", more valuable pieces.
"Run-of-kiln" production type pieces don't typically get sold with signed wooden boxes. Vendors will often add these with "post production" (not done by the kiln....done by the vendor) boxes that bear a caligraphic description of what is in the box ....ie. ぐいのみ....., and the kiln location name....sometimes using a red stamp for this. To someone who cannot read Nihongo (Japanese) it can LOOK like an artist signed box... but it is not. And it is not intended to; these boxes are made for the Japanese market... and it is expected that the person purchasing the piece (with box) reads Nihongo.
Signed wooden boxes are usually reserved for the more one-of-a-kind or the exhibition works, that almost always have involved the hand of the master potter in a significant part of the genesis of the piece.
Sometimes a box is done for a specific piece by someone other than the artist, typically after his/her death. This is typically reserved for famous artists and pieces. This person creating the box might be a former deshi of the artist if they are successful enough, the potter son of that artist, or a noted expert in the field of Japanese ceramics like maybe a museum curator. And the box will bear the fact of how it was created.
Each potter makes a personal decision about at what quality and price point level his/her work routinely warrants such boxes included with the pieces. Lesser known artists likely will do this for works at a price point that someone like a Matsuzaki Ken (look him up... he's great) would not consider.
To REALLY know if the pot is the real thing from the artist you think it is, and that BOX the pot is in is the real thing from the artist you think it is, requires either depending on the trust in a good reputable dealer or agent, or knowing both the artist's work and (reading) the artists' caligraphy and personal hanko (stamp) very, very well. Lots of study and practice.
And as we've seen here.... sometimes the boxes look SO bad.... that you don't really need to be an "expert" to detect something is wrong.
best,
..................john
PS: I already told Chip this ... but I wrote (in Japanese) the the guy on Ebay asking if another "Seigan" piece he has listed comes with a box SIGNED BY Seigan. No answer so far

.