The thing with terms like "at the Border-hold", "at any version of the Border-hold" and "all versions of the Border-hold" is that they're not clearly defined.
According to the quote from CoE Digest #107 it doesn't matter that LGS mentions "Border-hold" instead of "site", it still affects any site with the same name. So let's assume that "Border-hold" could just as well be read as "site". Some examples of the terms:
Spies Feared wrote:Scout or Ranger only. Playable on a Shadow-hold if one of your scouts is there or on a Ruins & Lairs if one of your rangers is there. An automatic-attack is created at the site against minion companies: Orcs - 5 strikes with 8 prowess (detainment). Additionally, automatic-attacks at the site are duplicated (including the new one) against all companies. Discard when site is discarded or returned to your location deck.
Here "at the site" refers to all sites with the same name.
Vile Fumes wrote:Technology. Playable at a tapped or untapped Shadow-hold, Dark-hold, or a site with a Dwarf automatic-attack. Discard during the site phase at a Border- hold or Shadow-hold to make all versions of the site Ruins & Lairs. Its normal automatic-attacks are replaced with: Gas - each character faces 1 strike with 7 prowess (cannot be canceled). Keep Vile Fumes with the site until the site is discarded or returned to its location deck.
Here "all versions of the site" also refers to all sites with the same name.
Guarded Haven wrote:Playable on one of your Wizardhavens other than Isengard, The White Towers, or Rhosgobel. The site is protected. Cards that give marshalling points are not playable at the site by your opponent in all cases. A company moving to or from this site is not considered to be moving through the region containing the site (including one less of its region type in their site path). Cannot be duplicated on a given site.
And here "at the site" again refers to all the sites with the same name.
The difference in terms seems very vague, if it even exists.