Given a concept, I name that concept "Gloop" and make it part of a defined word in the "English Language."
Given a concept, I name that concept "Gloop pattern" and make it part of a defined word in "Design patterns."
Both actions have the potential to fulfill either goal you describe above depending on the definition(s) of gloop and "gloop pattern."
Independent of the definitions or assuming both mean the same thing, the two actions are one in the same. There is no benefit of using one technique over the other.
Let's give you another angle: Defining a term under the umbrella of "Design patterns" doesn't make that definition any more precise than if you defined that term under the umbrella of the english language. There is no difference period.
Design patterns is shared vocabulary. English is also shared vocabulary. But the words "Design Patterns" is part of the "English Language." By creating the term "Design patterns" in the "English Language" you are essentially recursively adding complexity to the english language by defining a redundant concept in the same concept.
Just use english. Define the pattern in english, there is no need to define the pattern in "Design patterns."
Additionally, many patterns are better described with existing english words. Why use Facade pattern, when you can just say Object wrapper. The word "Design patterns" inserts a sort of false formalism and elitism into what is essentially just creating new vocabulary in the english language. The claim I'm making in this paragraph is that while yes it's good to have some formal nomenclature, it's excessive to give all of these patterns their own names. Let the naming and the definitions flow naturally.
Other fields of programming have patterns but they don't try to turn these patterns into some kind of theoretical field with it's own nomenclature. Currying is just currying nobody calls it the "Curry pattern". Recursion is just recursion, nobody calls it the "Recursion pattern."
I think you would have loved our study group. Especially the early years.
My personal position on the value of the art of namings, eg Facade, Proxy, Wrapper, Adapter, was somehow capturing the author's original intent. As distinct from the implementation. How it's meant to be used.
Lofty sentiment coming from someone condemned to decades of code maintenance.
Professionally, methinks design patterns, and their misuse, has been mostly detrimental. Maybe because the notions were taken too literally, treated prescriptively rather than descriptively.
Calling everything a Decorator. When it's actually a Chain of Command. And when you try to patiently explain the evils of silent failures, buried deep in the levels of indirection, to the "senior architect" author, that same architect insults your intelligence and walks off.
The mere utterance of Factory and Singleton in public somehow empowering legions of noobs littering entire organizations (and libraries) with innumerable implementations.
Trying to debug something called a "Write thru Cache" when its anything but.
But older me now understands every generation goes thru a phase where they think they newly discovered sex.
When I asked my then teenaged son the difference between "emo" and "goth", he informed me that "goth" is for old people.