I know 洋{よう}服{ふく}箪{だん}笥{す}, 衣{い}装{しょう}箪{だん}笥{す} and ワードローブ, but I've never seen them used and I don't know what the difference between them is.
I mean a typical wardrobe with doors (like the one from "The chronicles of Narnia").
I don't think there are strict distinctions, at least in the ordinary language, but the word you are looking for should be クローゼット.
For example, IKEA has the following categorization. タンス for chests and ワードローブ・クローゼット for the ones with 'a door'. You can use ワードローブ, too, but I feel it is less common.
More precisely, you can actually use タンス, too. I suppose タンス covers the two categories above, but クローゼット should be usually the ones with doors (or a separate storage room for clothes).
The door type is called 観音開{かんのんびら}き. So 観音開きの箪笥 could be used, but normally people are not that specific and タンス may be too generic. Hence クローゼット could be better (though the ambiguity with storage room remains). Probably ワードローブ doesn't have this ambiguity. (Again, I don't think people use these words so carefully.)