Decipher and the Star Trek CCG community really made this confusing.
During the initial distributiion and salles this set was called Star Trek: The Next Generation C.C.G. & as the box states it was a limited edition. Decipher did two other pint runs of this same set with each subsequent print run having a white border. The packaging for these print runs did not contain "Limited Edition". The first one was done in December of 1994 and was full of errors. Collectors and players have given this printing the name of "Alpha". Decipher did another print run of the same cards but fixed all the errors in 1995. This print run also has a white border. Collectors and players call this one "Beta". All three of these sets consist of the same cards just different variations. They weren't refered officially refered to as "premiere" until much later.
Decipher acquired the liscense to use Deep Space Nine several years later and then they dropped the "The Next Generation" from the name of the game. When they sold the products for the Deep Space Nine expansion they sold "limited" "Deep Space Nine" cards that also included booster packs of the "Premier" release (reprints from the original set). That's when the Premier name came into being. They also produced booster packs that were labeled "white border", to refer to the "premier" cards.
1st Edition refers to the rules and guidelines of the game itself. During the production of the first 12 or so expansion sets the cards Decipher made kept "breaking" the game and Decipher had to keep updating the rules. Eventually the rules got so complicated they basically had to start over.
Thus the creation of "2nd Edition". None of those names: Premier, Black Border, 1st Edition, or 2nd Edition have anything to do with the actual name of this set at the time of sale and distribution.
My two-cents is worth slightly more than a penny.
-- Chad --