pronouns - How do I identify subjects when quantities are involved?

I'm working my way through The Blue Book of Grammar and Punctuation, and I came across a difficulty.

In one of the quizzes, the book asks you to identify the subjects and verbs in sentences, and correct disagreements where necessary. Here is one such sentence:

Her attitude is one of the things that's different.

I incorrectly viewed one as a subject in the sentence above, which caused me to miss that things is actually the subject and so the verb should be conjugated are, and the sentence constructed thus:

Her attitude is one of the things that are different.

With me? I'm not 100% clear here why things is the subject and not one, but okay. I understand close enough.

Then I came to this explanation in the section on pronouns. The rule is copied to give context to the example and its explication.

Rule 5. The pronouns who, that, and which become singular or
plural depending on the subject. If the subject is singular, use a singular verb. If it is plural, use a plural verb.

Example:
He is the only one of those men who is always on time.

The word who refers to one. Therefore, use the singular verb is.

Here is where my confusion truly enters the picture. If who as a pronoun is referring to one in this sentence, then one is the subject (as is He). If one is the subject in this sentence, why is it not the subject in the previous sentence?

Thank you for your help! Let me know if I need to clarify my question.

Answer

This isn't a question of quantity, necessarily, but rather one of adjunct phrases.
Let's take your two sentences, with some phrase boundaries.

Her attitude is [[one] [of the things that are different]].

-

He is [[the only one [of those men]] who is always on time].

In the second example, he is the only one who is always on time out of a set of men (the rest of whom are always late). Therefore, the verb is singular to agree with "only one."

This contrasts with your first example, where "her attitude" is one of the set of things that are different.

In the first sentence, "to be" is embedded within the prepositional phrase "of the things that are different," whereas in the second, "to be" is not part of the prepositional phrase "of those men."

For example, you could say:

Her attitude is one of the things that are different about her, and I like it.

You don't say "them" like you would in "Her earrings are one of the things that are different about her and I like them."