Hi, requirements are a type of need, but the word "requirement" denotes something more formal and structured than just a need. If the question at hand has anything to do with formal documents or processes (patent law, applying for a school, job interview, legal issues, citizenship, contracts, etc), then almost certainly the preferred noun will be "requirement."
Here are some examples of how these concepts are related as verbs.
(On both sides of the equal sign, the sentences mean the same exact thing.)
I am *required* by law to register my car. = I am *obligated* by law to register my car.
So, I *need* to register my car. = So, I *must* register my car.
I *need* to because I am *required* to do it by law. = I *must* do it because I am *required* to do it by law.
It is a *requirement,* so I *need* to do it. = It is a *requirement,* so I *must* do it.
Hope that helps a little!