In the German gaming magazine PC Player (issue 01/1997) Privateer 2: The Darkening received a special award for the "Best FMV Cutscenes in 1996".
Origin also released a Deluxe Edition for Privateer 2, and it contained, besides all the regular edition items, a large-sized poster of the cover picture and a military-style badge (to sew on a jacket, i.e.). It is somewhat rare and sought after.
For as much of a new game as it is, there is at least one nod to the original Privateer in the sequel. There's a random mission in which you have to approach and identify a derelict starfighter. Nothing major, but upon contact with the ship you'll see that it's a 3d-rendered version of the Talon, the singlemost common ship in the original Privateer. Look for it in the manual also.
A very strong rumour (read: unproved but very strongly backed) says that in a a post Wing Commander 3 press release Origin had prepared a 3 space-sim lineup on the wake of WC3. Wing Commander 4, Privateer 2, And a little british game already in development called "The Darkening".
Subsequently thanks to WC4's humongous budget and the fact that The Darkening already had a working rendering engine and was in Beta. Privateer 2 got scrapped, and the Darkening became what we know now as Privateer 2.
Furthermore, it seems that original promotional material for Privateer 2: The Darkening referred to the game simply as "The Darkening", offering further indications that Erin Roberts' game was christened a sequel to Privateer after it was completed.
The storyline has nothing to do with the original Privateer or the Wing Commander universe other than the fact that you're a privateer.