!! Indeed, there is no story continuation that I remember but basically it is the same game engine and, lets say, inspiration. Play both in succession and you extend the same experience. It is four games (plus the variations I cannot yet fully discern), or a single game experience making it a single game in four installments. But what I d like to know now is what are the 400 enhancements mentioned in the EE versions.
The main difference between Baldur's Gate 1 & 2 and Icedwind Dale 1 & 2, is that in Icewind Dale you create the entire party versus just one character in the BG games and recruit the rest. Also, Icewind is more action/fighting oriented than the BG games are.
The main new things in the enhanced editions are 4 new NPCs in each game. Each character has their own quests in new areas too. Plus, the enhanced editions are made to run on modern computers without any tinkering. And some tweaks have been made to various things, like gems that are the same stack and you can have 80 arrows in a bunch instead of 20 in unmodded BG. Also, Baldur's Gate 1 is basically using the Baldur's Gate 2 engine. There are also some new character classes you can play in the Enhanced Editions. I hope this answers your questions.