Distinction with phrases.

The family devoured Aunt Lenora's carrot cake, their fingers scraping the leftover frosting from the plates.

(absolute clause) is missing finite verb but has subject like a noun phrase ?

Is this the same thing or wrong?

The old lady struggled to cross the road, adults ignoring her, when out the blue a child offered to assist her, the child clearly bettering us here.

noun phrase.

The couple were taking care of Max, the dog whining for a treat.

Apart from the non-finite nature of the absolute clause what distinguishes it from a noun phrase as they both have a subject (a noun).

What does this mean? The noun phrase is made up of various other phrases within them? But they are still noun phrases.

http://www.chompchomp.com/terms/nounphrase.htm

Modifiers that come after the noun might include prepositional phrases, adjective clauses, participle phrases, and/or infinitives.

Prepositional phrases: a dog on the loose, the dog in the front seat, the dog behind the fence

Adjective clauses: the dog that chases cats, the dog that looks lost, the dog that won the championship

Participle phrases: the dog whining for a treat, the dog clipped at the grooming salon, the dog walked daily