OK... I've had a few more Cups of Joe also.
Thread Form is the Geometry of the Thread. There are all kinds of Threads. Square Thread. Acme Threads. Pipe Threads. etc.
Unified Threads are Very Common here in the States. They have a Symmetric 60 degree Included Angle on the Thread and on the "Valley".
Of the Unified Threads, The Most Common are Unified Course (UNC) and Unified Fine (UNC). There are other Less Common Unified Threads like Ultra Fine (UNUF) but most of what you see in a Home Center or General Hardware Store is either UNC or UNF.
If I'm going to design something, and can use Any Thread Form, I'm going to chose Unified Threads because it is Easy to get Tap and Dies to cut the Threads.
And I'm going to chose Either UNC or UNF threads because I can Easily Buy things off the shelf that will screw onto the threads I cut.
In 7/8", Course Threads is 9 TPI (Threads per Inch), 7/8-9UNC. And Fine is 14 TPI, 7/8-14UNF.
So if I was doing it, and it didn’t matter what Thread Form I could use and Loading wasn’t a Factor, like in a Tube to carry Current, I would use 7/8-9UNC. Course threads are Slightly Easier to Cut. And Course Threads are found in More Common Applications so I might be able to use the Die for something else down the road.
Not saying that this is a Good or Bad Die. It was just the First thing that came up on Amazon.
Union Butterfield 2010(UNC) Carbon Steel Round Threading Die, Uncoated (Bright) Finish, 2" OD, 7/8"-9 Thread Size: Amazon.com: Industrial & Scientific
Hex Dies are Nice because you can turn them with a Wrench verses having to buy a Big Die Handle.
Union Butterfield 2025(UNC) Carbon Steel Hexagon Threading Die, Uncoated (Bright) Finish, 7/8"-9 Thread Size: Amazon.com: Industrial & Scientific
Once a Thread for is Chosen, Now I need to think about Drill or Stock Size.
For an External Thread, the OD of the Material you start with will become the Major Diam. And the Die will Cut the Minor Diam.
If you scan down this Chart you’ll see that for a 7/8-9UNC 2A Thread that the Major Diameter should be between .8731” and .8592”. (The larger the Major Diam, the Great the Thread Height, Stronger the Thread, Harder to Cut, Harder to Thread. Visa Versa for a Smaller Major Diam.)
But here's the Deal. A die Isn’t Designed to cut Diameters Much Larger than the Major Diam.
You Can't use a 7/8-9UNC on a Piece of Material that is say .950” Diam. And if you use it on a piece of Material that is Smaller than the Low Limit of the Major Diam., you Don’t get a very good thread.
Check out this Thread Chart for Reference.
Unified Screw Threads, Standard Series
There are numbers in your Post that I don’t understand. They sound like OEM or Vendor Numbers.
And I Don’t Trust Vendor Numbers. What you have to do is to get out a Mic and Physically Measure what you are Actually going to Thread.
Hope some of this Helps or at least, makes some sense.
BTW – When you do cut your Thread, Don’t forget to Chamfer the End of your Material to form a Lead Thread. So many people Forget or Don’t know to do this. And then wonder why it is so Hard to Get the Thread Started.