Looking for some help understanding these three coins...

Coin Finder

I do not own them.

Specifically, what are the "w" numbers on the slabs mean and

How do we know at lease one of these was struck by the "Confederate States"

Why are they labeled differently?

Thanks in Advance

yosclimber

W-07 and W-14 are identified die marriages for the 1861-O.
W stands for Randy Wiley, who with Bill Bugert wrote the 1993 attribution guide for Liberty Seated Half Dollars,
and assisted with the newer guides where Bill Bugert is the sole author.
Usually I see these as WB- numbers.
However, for 1861-O they are W- numbers, because Randy Wiley published the die emission sequence for this date in 2005 and used W- numbers at the time.
http://www.lsccweb.org/Links.shtml
See pages 457-492 of Bill Bugert's Volume IV guide (New Orleans) for the 1861-O die marriages. It is a free PDF file.
http://www.lsccweb.org/BillBugertBooks/BillBugertBooks.php

How do we know at lease one of these was struck by the "Confederate States"

Randy Wiley figured out the die emission sequence and correlated it with dated documents on mintage quantities by using die usage estimates from nearby dates.
From page 463 of the PDF:

die marriage | authority | date
W-01 - W-02 | USA | January, 1861
W-03 - W-08 | State of Louisiana | February-March, 1861
W-09 - W-15 | Confederate States of America | April, 1861

Randy Wiley's original 2005 Gobrecht Journal #94 article is at:
https://archive.org/details/gobrechtjournalfn094libe/page/2

A fairly complete set of these die marriages was up for sale recently at Gerry Fortin Rare Coins, and several are still available.
http://seateddimevarieties.com/FS_Seated_50C_1856_1891.php
You can also look up the ones that sold in the past:
http://seateddimevarieties.com/SalesArchive.html

Coin Finder

Thanks Yos! Anything about the other question about the confederate states?

yosclimber

@thebigeng said:
Thanks Yos! Anything about the other question about the confederate states?

My edits continued, and my revised post above should answer your question about the CSA.

oih82w8

@thebigeng said:
Thanks Yos! Anything about the other question about the confederate states?

Here is a little snip-it from Gerry Fortin about a W-14 Confederate issue;

1861-OW-14Die Crack Bisected Date / Speared Olive Bud

"Struck under the CSA administration during April 1861. The W-14 die pairing consistent of a late die state obverse paired with a fresh reverse die. The obverse is well known for having a vertical bisecting die crack through the date while the reverse has two parallel die lines through an olive bud. The latter is now known as the Speared olive Bud reverse and is used in final die pairing (W-15) before the New Orleans mint is closed. "

http://www.seateddimevarieties.com/FS_Seated_50C_1856_1891.php

Coin Finder

Thanks guys that helps!

RogerB

RE: "The latter is now known as the Speared olive Bud reverse..."

Also known as the "Dry Martini" reverse....