Is it considered a lie to exaggerate in speech, such as saying "I waited for you a year" when intending to express a delay, or to change details of a story unintentionally and without altering its meaning?

What is mentioned in the question is not considered a lie. The first is an exaggeration, which is a form of metaphor, like: "And the head flared up with old age." As for the second, which is narrating the story with different wording while preserving the meaning, it is not a lie. Scholars have permitted narrating hadith by meaning, so narrating a story is even more permissible.