2300AD was the second edition.
There were slight rules changes in a couple of places - mostly combat IIRC - and a lot more background info for the game.
T2300 has a 48 page Player's manual and a 49 page Ref's guide.
In 2300AD you get a 94 page Adventurer's Guide and a 110 page Director's Guide.
What Sigg said. 2300AD is basically the second edition of T2300. And it firmly separates it from the Traveller universe (which it was never really part of to start with. Quite why some people still claim that they're playing Traveller because they're playing 2300AD or T2300 is beyond me).
Back in the day, there was a half-assed attempt at GDW to link the continuities of Twilight 2000 and Traveller vis T2300, but it never quite fit right. At least that was the original intent, but the fit was never too good, so the idea was left out in the rain to die.
Oh, it's an extension of Twiight 2000. It just never fit with Traveller itself in the first place - even T2300 had completely different aliens and first contact scenarios to Traveller. The Vilani weren't found at Barnard's Star, for example, and I think humanity moved into space a lot sooner in 2300 than in Traveller anyway.