In the first sentence,
It had snowed in the night...
the past perfect "had snowed" implies that the night has finished, and thus implies that the bus that was supposed to arrive in the morning did not arrive in the morning.
In the second sentence,
- It snowed in the night...
the night might not be done yet, from the writer's point of view, and the bus that "didn't arrive" might have been expected sometime during the night. Not necessarily, buf maybe.
If one wanted to more clearly suggest that both the snow and the "not arriving" occurred on the previous night, one could say:
- It had snowed in the night, so the bus had not arrived.
The interpretation also depends on how long you think the writer might have been willing to wait for a delayed bus before declaring that it "didn't arrive" (or hadn't).
This is a common misunderstanding. Your sentence mentions an action. That action seems to be in the past. The statement uses the present tense. Why?
Some verbs express action. Other verbs express state of being*. The verb "to have" expresses a state of being.
1) I saw the film.
2) I have seen the film.
3) I had seen the film.
In 1), the only verb is a past-tense action verb.
in 2), there are two verb words which form a single verb phrase. The "have" is a present-tense state-of-being verb. The "seen" is a verb without any tense but with the perfect aspect. This form does not express the action of the verb "to see". It expresses the result of that action.
I have seen the film. I possess a result of the action.
In 3), the "had" is a past-tense state-of-being verb.
The structure of 3) is rarely used on its own. Often, it's used to suggest that one thing is even further in the past than another:
4) I had seen the film when I read the book.
The action of "to read" is in the past. At the time of the action of "to read", my state of being included the result of the action of "to see". This suggests that that action of "to see" happened before the action of "to read".
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* As far as I can tell, we use the phrase "state of being" because the word "condition" would be confusing. Verbs like "to be" and "to have" express a condition in the sense of "the way things are", rather than the sense of "something required for something else". We use the word "condition" in the second sense when discussing subordinate clauses, so we use "state of being" when discussing what a verb can express.
Best Answer
Interesting question, the meanings are very similar, for the difference is context.
I didn't sing the song - This is a sentence that can stand alone, in response to a question or as a statement of fact.
I had not sung the song - This phrasing would typically be used in context of another event, or as part of an explanation to a series of events. On it's own this sentence would seem strange.
i.e. "Until I knew the tune, I had not sung the song"