I don't see the (relevant) difference. DLC is downloadable expansions. Additional content is all good by me however it gets to me.
DLC is downloadable content, which is exactly what it sounds like, it's simply additional content that can be downloaded, in the current terms used in the industry, DLC is basically mods, except it costs money. Expansions, on the other hand, are traditionally reletively large addons, look at Shivering Isles for Oblivion or Tribunal and Bloodmoon for Morrowind, for example, both have a fairly large amount of new content, and usually that's where the distinction lies, it comes down to a matter of scope. DLC may be quite small, anything from a suit of armor or a new weapon to a fairly short questline that might take a few hours and may add new locations to explore can be DLC, on the other hand, expansions have to be fairly major, with many new locations to explore and such, in a game like the Elder Scrolls, they'll typically have a new main quest and many new side quests, and new enemies and items, and may even have things worth seeing after you've completed the quests involved, with say... Knights of the Nine, once you finish the quests, it's over, aside from the items you get as a reward, you can pretty much ignore it after that. Also, expansions don't have to be downloadable, they may also be available only on DVD. Thus, expansions may or may not be DLC, but DLC is not expansions.
Although they don't really have to be mutually exclusive, after all, Oblivion had an expansion and some DLC, there's no reason Skyrim can't as well, that doesn't mean it will have both, but it could. Though if it comes down to a choice between the two, I'd go with expansions any day, because there's no way a small downloadable addon can add as much as a full expansion, and even if the developers create enough DLC to offer the same amount of content as an expansion, it still won't be as satisfying because it comes in the form of small individual addons that are not mutually connected and are limited in what they can do by their very nature, and the combined price of all DLC would probably cost a lot more than an expansion too. Unfortunately, it seems like Bethesda has decided to do otherwise, unfortunate, but I guess that's just the trend the gaming industry is moving towards, and this will continue as long as releasing many small, seperate addons continues to be more profitable than one or a small amount of extensive expansions.