I think of it like this: In English, "Clad" is a (somewhat old-fashioned) term describing the general style of dress. e.g., "clad in uniform" or "skyclad" (the latter meaning "naked"; clad in nothing at all). So, kläder = the clothes that one wears, regardless of what articles they actually are. By contrast, I think of "klänning" as associated with the term "dressing gown". That is, "klänning" = a particular item of clothing that one wears to "dress up" in.
I am a native English speaker and I haven't learned enough yet to know whether any of these associations are "correct" according to etymology, but that's just how I keep the two words straight, in my own mind.