MShipley88 wrote:There is a book that claims to be a wizard logo 6th print, January 1980 Players' Handbook in the lot.
This is not new, unless I've missed your point completely. As per the Acaeum listing, the 6th through 10th printings (and there is more than one 10th variant, if memory serves correctly) all claim to be the 6th printing. Copyright pages are not to be trusted.

Assuming the Acaeum listing is undeniably, unerringly accurate, which printing do you have?
Quick Check:
6th = orange endpapers, wizard
7th = white endpapers, wizard
8th = white, face logo
9th = white, angled TSR logo
10th = Easley cover, angled TSR logo (at least three variants)
11th = states 11th.
And so you see the problem. The 6th states it's the 6th. The 11th states it's the 11th. Everything else needs to be sandwiched between these two or it'll
really get confusing.
The listed printings as detailed above allow for the
major differences to be noted; variants absolutely exist within those guidelines. Don't take the word "printing" too literally; we're using it more in the sense of "class".
I swear, this book looks totally different from my other wizard logo 6th print
It's unfortunate that we're working with the 6th printing because of all the confusion it brings. Getting into fine-grain taxonomy, if you've got two books that fit in the same printing, but are not identical, you're looking at two variants within the printing.
Some generic things I try to compare across variants:
1. ISBN - (back cover, spine, copyright page)
2. Spine - (everything)
3. Catalog page (look at everything, particularly prices)
4. Copyright page (look at everything)
5. Use of TM vs. (R) - (Front cover, copyright page, catalog page, spine)
Colors/inks/paper/texture variants are
much tougher to confirm than printing variants, because they're more subtle/subjective. Try to find a textual difference if you can.
N.B. While I find this stuff fascinating, it's unlikely to make the Acaeum
PHB page -- minor variants just add to the already confusing chronology.