To me, a "folio" is a collection of loose, unbound prints defining a content that is more like a book than a random stack of unsequenced prints. In my folios, I use a title page to lead things off, then typically a statement about the project, the images pages come next, sometimes an afterword is appropriate, and the last page is a colophon. They are sequenced, like a book, but loose, like a portfolio. It's my answer to the problem of how to include original prints in a book without doing tip-ins. I can do this type of presentation with gelatin silver prints, photogravures, inkjet prints — literally any flat sheet or image. I can include a sewn text signature or French fold component. I can even include a CD if it's called for in the project. It's turned out to be quite a flexible design idea that allows all kinds of individual adaptations.
I'm currently using a folio cover that is die-cut with a hole that allows me to place a title page behind the cover, showing through. This allows me to produce a large quantity of covers (amortizing the costs involved), and make folios for any project from one copy to hundreds. Again, flexibility is the key to the design.
I've never actually seen anything quite like the folios I produce, so there really isn't a term for it. I've been forced to make my own definition. I even tried to find a Latin root that I could adapt, but folio seemed the best, so that's the word I use. I've used this term since 1992 when I made the original Made of Steel folio.
The cover is made from an acid-free archival art paper. My favorite that I use time and time again is Gilbert Oxford in the heaviest 100# Cover. It comes in a variety of very rich and perfect colors.
The assembly uses only archival, acid-free materials to protect the life of the prints and pages inside. Each folio is shipped in a sealed, plastic sleeve.
In my personal work, folios are numbered in an open editions — a description of this numbering can be found here. I sign the title page and hand-number the colophon.
From the success of the folio concept in my personal work, it was not a large leap to realize that this idea could be adapted for the presentation of collections of prints from our LensWork alumni. It's worth noting that we've published both b/w and color LensWork Folios!
Here is a short history of the LensWork Special Editions program which now includes offerings of folios by various photographers who you've seen published in LensWork or LensWork Extended.