Liberty is the state in which people can act and speak freely, and equality is the state of being equal in rights and opportunities. Just because a person is afforded certain liberties does not mean the person is given equality.
In America, as long as what a person says does doesn't offend, take away rights from or harm another person, the person is given liberty. This is one of the core values of the country. Equality is another core value that is meant to give every person in the country the same opportunities as every one else. Everyone should have the right to participate in the political process, enjoy economic success and generally live fulfilling lives.
An example of liberty is journalism. For good or bad, as long as a journalist doesn't make libelous or slanderous comments designed to hurt a person or group of people, the journalist can utilize freedom of the press and talk about whatever he or she wants.
An example of equality is the ability to attend school. Everyone, regardless of their financial or ethnic background, has the ability to obtain an education. A school cannot discriminate against anyone who can perform the steps necessary to gain admittance and better themselves through education.