There's significant difference from a semantic point of view, more than structural/ grammatical.
Noun phrases with a verb or any other POS component are more explicit and 'simpler:'
lives in New York
Verb qualifies noun creating a new noun, 'New Yorker.'
On the other hand, nouns/ noun-phrases without this are implicit and 'enriched.'
Requires the reader to extract additional semantic content 'person' and 'having/ suffering from/ diagnosed with' that is not expressly stated.
There are no specific terms to describe these forms that I know of. However, the enriched form is used for brevity while the plainer alternative is better for improved readability.
In some cases, the semantics can be more taxing, especially in instances where the real noun is to be generated by a semantic synthesis, as in:
Author vs writes books
Neither 'writes' nor 'books' is the entity being referred. A Bahuvrīhi (बहुव्रीहि, Sk.) compound noun "that refers to a thing which is itself not part of the compound" WP