Often the words are interchangeble but I hope this helps.

Nude is the state of being without clothes. It is also the name of a color, skin color.

Naked is the state of being without clothes but can also be a feeling of vulnerability. Or it is something bare un hidden or covered. For example the 'naked truth' is the story with embellishment.

Correction:
For example the 'naked truth' is the story without embellishment.

Amplification:
"Nude" applied to people generally has some sort of positive aspect and is most often the result of deliberate choice.
-Artists paint nudes
-Nudists find doing without clothing is a positive lifestyle

"Naked" has other meanings, such as bloß, blank, offen, that nude does not. Siehe Wörterbuch: naked
-naked eye
-naked truth
-naked flame
-naked power
-naked hate
-the naked chef (=doesn't put sauces on food)

Other than the correction above, #1 is right, but I thought a bit fuller explanation might help others who read this.

I know this is an old thread, but it was referenced recently - Siehe auch: difference between "nude" and "naked"... - (which is how I came here), and I noticed
1. There was an error that needed to be corrected
2. The explanation could be a bit fuller

the naked chef (=doesn't put sauces on food)

Thanks, Robert! I never knew that.

I read once (but can't seem to find it now) that "naked" suggests being caught by surprise, while "nude" means it was done on purpose.