What issues differ from the Libertarian and Constitution Parties?

Answer 1

The stated platform of the Libertarian Party is consistent with elements of the philosophy of libertarianism, favoring minimally regulated, laissez-faire markets, and strong civil liberties.

The Constitution Party holds that the Republican and Democratic parties are becoming corrupt and are subversive in nature. It argues that America was founded upon Biblical principles. It advocates a stronger adherence to the original intent of the United States Constitution and the principles of the U.S. Declaration of Independence. It has a strong conservative approach on moral issues and seeks to restore what it calls the "Biblical foundations" of "American jurisprudence.

So I guess that the Libertarians are for less government involvement in every day life. While the Constitution Party is more for traditional morality enforced by government edict.