In the United States the higher education system is broadly categorized into Colleges and Universities.
Colleges
They are smaller than universities, and typically offer undergraduate degrees. There are several community colleges across the country that offer education at a lower rate, which offer a 2-year associate degree. Post this, you have the option to join a university and earn an undergraduate degree at a university.
Universities
In the USA, universities offer postgraduate, doctoral and post-doctoral degrees, and are classified into public and private universities.
Public universities are largely set up and managed by state governments and named after their respective states.
At a Private university, these comprise both profit and not for profit institutions which are funded by donations and tuition fees.