Yes, there's a difference in structure between
- Storing the data is important.
- Storing of the data was implemented using ABC.
Their subject constituents
- Storing the data
- Storing of the data
vary in an interesting way.
(2), but not (1), can start with an article
(ungrammatical examples are marked with an asterisk * )
- *The storing the data
- The storing of the data
Only noun phrases can take an article, which means that in (2) storing is a noun.
But in (1) storing is a verb -- a Gerund -- and the data is its direct object (therefore no preposition is needed). This becomes clearer with sentences:
- *The singing the "Star-Spangled Banner" starts at 9. (noun - can't take direct object)
- The singing of the "Star-Spangled Banner" starts at 9. (noun - OK with preposition)
- *Singing of the "Star-Spangled Banner" starts at 9. (gerund - needs no preposition)
- Singing the "Star-Spangled Banner" starts at 9. (gerund - OK with direct object)
You may have been taught that any noun that ends in -ing is a Gerund. This is not correct.
Gerunds are verbs and have verbal properties (like having direct objects);
nouns, on the other hand, have nominal properties, like taking determiners.
They may sound the same, but they don't act the same.