<p>When somebody says a "national university", it just means that it is a school that is well known to the entire country. Colleges can be public or private. Public schools are run by the states. Private colleges are run separate from the government. A "national university" could be either private (such as Yale) or public (such as UCLA.)</p>
<p>Financial aid works as follows: Each college has a COA (Cost of Attendance) that includes tuition, room & board, books and other expenses. Each applicant has a EFC (Expected Family Contribution) that is the money that the college expects you to pay. The EFC is calculated based on information that you supply on a FAFSA form. Your NEED is then COA minus EFC. The college will try to satisfy your need with a "Financial Aid Package". There are typically three components to the package:
1) Scholarships/Grants - this is a discount, it is just free money
2) Loans - this is money that you borrow and pay back after you graduate
3) Work Study - this is money that you earn for a part-time job connected with the college</p>
<p>The above is need-based aid. The vast bulk of financial aid is need-based, but it can also be merit-based where you win the money by being especially qualified.</p>