Second column is according to: https://help.libreoffice.org/7.2/en-US/text/shared/01/06040100.html. Third column is according to my own tests (examining the borders tab of the relevant paragraph or Styles Inspector) and according to https://opengrok.libreoffice.org/xref/core/sw/source/core/edit/autofmt.cxx?r=fea7b531#526 X = discrepancy.
--- 0.5pt single underline 0.05 pt single underline X
___ 1.0pt single underline 1 pt single underline OK
=== 1.1pt double underline 1 pt double underline X
*** 4.5pt double underline 4 pt thick thin small gap X
~~~ 6.0pt double underline 4 pt thin thick small gap X
### 9.0pt double underline 2.5 pt double (wider lines) X
No mystery about observed behavior.
1. The values on the help page correspond to the values found in autofmt.cxx in its initial checkin in 2000.
2. Source code changed at the end of 2010: https://opengrok.libreoffice.org/xref/core/sw/source/core/edit/autofmt.cxx?r=e93c59d0 but no explanation or bug number.
3. Changed again at end of 2013 with bug 71740, where attachment 89414 [details] gives a nice visual overview of the historical development, including the current appearance.
Clearly the help page has not followed up on the changes with bug 71740
@Stuart, is there a preferred terminology to refer to the line styles used by the AutoCorrect "Apply border" option?
For the first three, I will just keep single underline and double underline, but uncertain about how to approach the last three.
*** 4 pt thick thin small gap
~~~ 4 pt thin thick small gap
### 2.5 pt double (wider lines)
Here is current help page: https://help.libreoffice.org/7.2/en-US/text/shared/01/06040100.html
Created attachment 169375 [details]
current bottom borders available by autocorrect formatting
@Seth, yes this Help tweak is overdue.
The thick/thin and thin/thick 4.0 point (80 TWIP) simply are double lines, but asymmetrical in thickness. I would just label them that, a 4.0 pt "thick/thin double line" or "thin/thick double line".
And perhaps include a note that the TWIP <=> 1/1440", or 20 TWIPS <=> 1 PT, noting that the Paragraph bottom border Autocorrect applies is an actual measured height, that may be of single line or a double line composition. They are not scaled. 
### is 2.5pt or 50 TWIPS
*** OR ~~~ are 4.0pt or 80 TWIPS
=== O$ --- are 1.0pt or 20 TWIPS
--- is 0.05pt or 1 TWIP
The defined Line widths are as in 
Also, if needed, beyond these AutoCorrect presets, a broader range of bottom borders can be applied using the Paragraph dialog.
Created attachment 169390 [details]
screenshot for proposed description for Apply Border
(In reply to V Stuart Foote from comment #2)
Thanks for detailed and helpful information.
> Also, if needed, beyond these AutoCorrect presets, a broader range of
> bottom borders can be applied using the Paragraph dialog.
Has inspired a more differentiated presentation. Might make this option more interesting and useful for some (but have skipped the "twips" in the spirit of less is more, though fyi ).
See attachment for proposed version, which tries to minimize text changes (to avoid retranslation. (table layout is not representative of layout in help).
Good enough? Suggested changes?
(In reply to sdc.blanco from comment #3)
> Created attachment 169390 [details]
> screenshot for proposed description for Apply Border
much better, +1
Seth Chaiklin committed a patch related to this issue.
It has been pushed to "master":
tdf#140075 update table and help for Apply border option in AutoCorrect
Thanks for your help Stuart.