A dog pack is a simple singularity, whereas a pack of dogs has a hint of the potentially chaotic. A pack of dogs can run amok.
But it's not about dogs; this is really about pack and whether the modifier is a singular attributive adjective or a prepositional phrase with a plural noun.
A cigarette pack.
A pack of cigarettes.
With "a cigarette pack" we have a singular adjective and a singular noun. The nuance of the singular, if there is any, is monadic simplicity not in need of organization.
With "a pack of cigarettes" the modifier is in the plural which allows a hint of potential disorganization to poke its wet nose into the situation. Multiplicity wants organization.
Just as a pack of dogs can run amok, take a cigarette or two out of the pack and soon you have cigarettes leaning sideways, no longer standing perfectly parallel. Utter chaos.