In short, yes, that is my first impression that 'naked' and 'nude' are entirely unclothed. But it is not so clear cut as all that.
First, naked.
If you look at dictionary entries (OED is the best, but a reasonable view can be cobbled from many other online dictionaries, 'naked' ('nude' we'll get to in a bit) has multiple related meanings. The primary meaning, that is the one that is least metaphorical, seems to be not covered by any clothing at all. When modifying a body part, eg 'naked torso' it is only referring to that part. When referring to a person, this leads one to believe that the person is entirely unclothed (some dictionaries say 'not wearing any clothes', others '(of a person or part of the body) without clothes.'). If one were to say 'That man is naked' and you discover upon peaking through ones fingers that he is wearing nothing but a loin cloth, you might very well be indignant, take away your hand from your eyes and wonder what the big deal is.
But in former more embarrassed times, 'naked' used of en entire person, really could be used for only being partially exposed or only in undergarments. This usage is a bit dated (even obsolete) but is legitimate.
Also, there's always room for metaphor and hyperbole and context. A naked Amazonian dweller could be one whose only garment, a leather waist string slipped off his penis, but a naked Inuit in the frozen Canadian tundra might well be one who is only missing a hat.
So saying 'that person is naked' for someone who is not entirely unclothed sounds a bit Victorian. Surprising to our modern ears. But still legitimate. But still old-fashioned.
Since we're on the subject, I can't let this go without mentioning the somewhat relevant quip by Lewis Grizzard about the subtle differences in word meanings. Note that this depends on the subtle difference in formal and informal pronunciation in the Southern US.
There's a big difference between the words, ‘naked’ and ‘nekkid.’ ‘Naked’ means you don't have any clothes on. ‘Nekkid’ means you don't have any clothes on - and you're up to something.
As to 'nude', while often interchangeable with 'naked', there are no exact synonyms. Sure, 'naked' and 'nude' are pretty close, but dictionary definitions aren't the entirety of a word's usage. You don't visit a museum to view naked portraiture; that sounds like the paintings have no frames. Real estate lawyers don't deal with nude title to a property; that sounds like a civil rights lawyer's domain. But I suppose if 'Nude Lunch' were the title to Burrough's drug-addled novel, I suppose we'd all still think it's a salacious title for a controversial novel.
But to logical denotation differences, if there were a nude person on the beach, I'd expect that they are clothes-less entirely on purpose, whereas a naked person has the possibility their clothes were stolen and were a little chilly.