I would ask your question a bit differently.

First of all, the examples you give are verbs, not nouns.

In English, words often can have different parts of speech, and we can derive a noun from most of our verbs.  I don't know any exceptions!

For example - endure - endurance; reside - residence; bear - bearing.

Second, the gerund is the same word as the verb form called the present participle. It is created by adding the ending "-ing" to the verb.

A present participle that is used grammatically as a noun is called a gerund. For example, it can be the subject of a sentence, or an object.

A present participle can also be an adjective and describe a noun. 

There are cases where the present participle is a conjunction, preposition, or adverb! (Look up "considering")

These words have a meaning that is very closely related to their root verb.

The exceptions would be words that are spelled the same, but have drastically different meanings. (There are lots of these in English.) Also, a gerund may have developed a parallel, but different etymology from the root word. This can happen through natural language evolution.

Abide  does have the meaning of "wait patiently for", "to continue in the present state" so its participle, abiding, takes on a similar meaning.

His love is abiding and everlasting.  (His love abides in me.)