Gerunds are only ever verbs, never nouns
I think your mistake is pretending that any word that ends in -ing and which is derived from a verb is a “gerund”. This is not true. To be a gerund, it must be verb. And the first one is not:using is not gerund in first sentence. It’s only a noun—a deverbal noun, if you prefer. Nouns do noun things like taking articles, adjectives, and prepositional phrases.
For example, here taming is a noun only, not a verb, and therefore not a gerund:
- the quick taming of the shrew
You can tell it’s a noun not a verb because it’s doing noun things only, and it’s not doing verb things.
In contrast, here taming is indeed a verb with none of the customary nominal appurtenances:
This time taming takes an adverb not an adjective, has a direct-object argument, and accepts no article. That makes it a verb, not a noun. It is therefore a gerund. The other one is not.
But entire gerund phrases can replace entire noun phrases
A gerund phrase is a kind of non-finite verb phrase that is able to do the job of a noun phrase, including serving as the a clause’s subject and as a verb’s object complement or a prepositional object.
- Quickly taming the shrew is your best strategy. (gerund phrase as subject of copular verb)
- I recommend quickly taming the shrew. (gerund phrase as direct object of the verb)
- By quickly taming the shrew, you have restored tranquility in our household. (gerund phrase as prepositional object)
Those are gerunds, so only verbs not nouns. And those gerund phrases are not nouns, either, because you cannot do a noun thing to a gerund phrase even though a gerund phrase can itself do a noun-phrase thing. You have to look at these as replaceable constituents.
The other construction has no verb in it at all. It’s just a regular old noun phrase, not a gerund phrase.
- The quick taming of this shrew is your best strategy. (noun phrase as subject of copular verb)
- I recommend the quick taming of this shrew. (noun phrase as direct object of the verb)
- By the quick taming of this shrew, you have restored tranquility in our household. (noun phrase as prepositional object)