"Pass me the helmet," "Why not give me the helmet?" Both have the same purpose, but taken literally, they reveal a person's level of politeness and a lack of politeness.
However, this doesn't explicitly make someone who uses "give me the helmet" impolite. It could happen between close people who are accustomed to using harsh language, so it's perfectly normal. Depending on the tone of voice, it could be interpreted as assertive or rude.
So, for people who use more polite, refined, or educated language, "pass me" might be used more often, especially with people they aren't as close to or respect more. So, which is better, and should you use "pass me" or "give me"? Actually, the two don't have different meanings; it's fine.
The point is, if we want to appear more relaxed, "pass me" is more appropriate, and if we want to appear assertive, we can also choose "give me."